Exam Details
| Subject | ||
| Paper | paper 1 | |
| Exam / Course | ssc cgl combined graduate level | |
| Department | ||
| Organization | Staff Selection Commission | |
| Position | ||
| Exam Date | 01, August, 2010 | |
| City, State | central government, |
Question Paper
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SSC
Combined Graduate Level Tier-II Exam
Held on: 01.08.2010
1.
A General, while arranging his men, who
were 6000 in number, in the form of a square,
found that there were 71 men left over. How
many were arranged in each row?
73 77
87 93
2.
A number, when divided successively by
5 and leaves remainders 3 and 4
respectively. The least such number is
50 53
19 214
3.
A number, when divided by 296, gives 75 as
the remainder. If the same number is divided
by 37 then the remainder will be
19 31
4.
The square root of
3
(0.75)
2
..
0.75 .
(0.75) .
1.
.
.
1 .
0.75
5.
The sum and product of two numbers are
12 and 35 respectively. The sum of their
reciprocals will be
11 12 35
35 3512
1
1
6.
If a2 .
b2 ..
then the value of a2+ b2
2
2
a
b
will be
1
1
1 2
2
2
.
1 .
2
7. If .
x ..
then
.
x .
.
1 .
.
x3 .
3 .
is equal to
.
x .
0.1 .
0.1 .
0.1 .
0.02 .
0.02 .
0.02
8.
is equal to
0.2 .
0.2 .
0.2 .
0.04 .
0.04 .
0.04
0.125 0.250
0.500
0.855
1 100 1
9. If x .
then the value of x .
100 is
x
x
10.
If x3+ 3x2+ 3x then x is equal to
36
2
31
11. If 2x .
then the value of x .
3 is
x
x
1311 11 13
.
888 8
12. The greatest number among
357
2,3 is
34 73
5 52
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22
13. 3 (13.608) .
(13.392) is equal to
0.6 0.06
1.8 2.6
.
111 1 .
14.
...
.
... ..
is equal
.
1.
22 .
33 .
4 99 .
100 .
to:
1 99 100 1000
9900 100 99 99
15.
The sum of all the digits of the numbers from
1 to 100 is
5050 903
901 900
16.
A shopkeeper sells suger in such a way that
the selling price of 950g of sugar is the same
as the cost price of 1 kg of sugar. What is his
gain per cent?
51
1
5 4
195
19
17.
A person bought a horse and a carriage for
Rs. 20000. Later, he sold the horse at 20%
profit and the carriage at 10% loss. Thus, he
gained in the whole transaction. The cost
price of the horse was
Rs. 7200 Rs. 7500
Rs. 8000 Rs. 9000
18.
A sells an article to B at 15% profit. B sells it
to C at 10% loss. If C pays Rs. 517.50 for it
then A purchased it at
Rs. 500 Rs. 750
Rs. 1000 Rs. 1250
19.
An article is sold at a certai fixed price. By
2
selling it at of that price, one loses 10%.
3
The gain per cent on selling it at the original
price is
1
20 33
3
200
40
9
20.
A sells an ariticle to B for Rs. 45,000 losing
10% in the transaction. B sells it to C at a
price which would have given a profit of
10% to A. By what per cent does B gain?
75 100 200 150
239 7
21.
The cost price of an article is 80% of its
marked price for sale. How much per cent
does the tradesman gain after allowing a
discount of 12%
20 12
10
22.
A merchant has announced 25% rebate on
prices of ready-made garments at the time
of sale. If a purchase needs to have a rebate
of Rs. 400, then how many shirts, each
costing Rs. 320, should he purchase?
23.
A merchant purchases a wristwatch for Rs.
450 and fixes its list price in a such a way
that after allowing a discount of he
earns a profit of 20%. Then the list price (in
rupees) of the wristwatch is
500 600
750 800
24.
A reduction of 10% in the price of tea enables
a dealer to purchase 25 kg more tea for Rs.
22500. What is the reduced price per kg of
tea?
Rs. 70 Rs. 80
Rs. 90 Rs. 100
25.
Ram donated of his income to a charity
and deposited 10% of the rest in a Bank. If
now he has Rs. 8640 left with him, then his
income is
Rs. 12,500 Rs. 12,000
Rs. 10,500 Rs. 10,000
26.
If the length of a rectangle is increased by
10% and its breadth is decreased by
then its area
decreases by increases by
decreases by
remains unchanged
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27.
Three spherical balls of radius 1 cm, 2 cm
and 3 cm are melted to form a single
spherical ball. In the process, the loss of
material is 25%. The radius of the new ball
is
6cm 5cm
3cm 2cm
28.
IfA C 5andC: D =5:9,then
A D is equal to
11:17 8:27
9 9
29.
If the length of a rectangle is increased in
the ratio 6 7 and its breadth is diminished
in the ratio 5 4 then its area will be
diminished in the ratio
17: 16
8 7
30.
7 years ago, the ages (in years) of A and B
were in the ratio 4 and 7 years hence they
24 36
48 60
32.
C are partners in a business. During a
particular year, A received one third of the
profit, B received one fourth of the profit and
C received the remaining Rs. 5000. How
much amount of money did a receive
Rs. 1000 Rs. 3000
Rs. 4000 Rs. 5000
33.
Three horses are tethered at 3 corners of a
triangular plot of land having sides 20m,
30m and 40m each with a rope of length 7m.
The area (in m2) of the region of this plot,
which can be grazed by the horses, is
.
22.
.Use ..
.
.
7 .
77
75 77 80
3
34.
A wire, when bent in the form of a square,
encloses a region of area 121 cm2. If the same
wire is bent into the form of a circle, then the
area of the circle is
.
..Use ..22
7
.
..
150 cm2 152 cm2
154 cm2 159 cm2
35.
The ratio of the area of a sector of a circle to
the area of the circle is 1 4. If the area of the
circle is 154 cm2, the perimeter of the sector
is
20cm 25cm
36cm 40cm
36.
The length of the diagonal of a cube is 6 cm.
The volume of the cube (in cm3) is
183
283
243
303
will be in the ratio 5 6. The present age of B
is
56 years 63 years
70 years 77 years
37. If a sphere of radius r is divided into four
identical parts, then the total surface area of
31. Two numbers are such that their
the four parts is
difference,their sum and their product are
4
.
r2 square unit (b)2.r2 square unit
in the ratio of 1 7 24. The product of the
numbers is
(c)8.r2 square unit (d)3.r2 square unit
38.
A sum of money, deposited at some rate per
cent per annum of compound interest,
doubles itself in 4 years. In how many years
will it become 16 times of itself at the same
rate
16 12
10
39.
What is the difference between the
compound interest and simple interest on
Rs. 4000 at per annum for 2 years
10 11
20 100
40.
The simple and compound interests on a
sum of money for 2 year are Rs. 8400 and
Rs. 8652 respectively. The rate of interest per
annum is
7.5% 4.5%
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41.
A man can row against the current three-
fourth of a kilometre in 15 minutes and
returns the same distance in 10 minutes. The
ratio of his speed to that of the current is
5 3
5 1
42.
Two places A and B are 100 km apart on a
highway.One car startsfromAandanother
from B at the same time. If the cars travel in
the same direction at a constant speed, they
meet in 5 hours. If the cars travel towards
each other, they meet in 1 hour. What is the
speed of the car running faster
60 km/hr. 50 km/hr.
111 1
234 5
48.
The sum of the areas of the 10 squares, the
lengths of whose sides are 20 cm, 21 cm, ....
29 cm respectively is
6085 cm2 8555 cm2
2470 cm2 11025 cm2
49.
The square root of
9.5 .
0.0085 .
18.9
is
0.0017 .
1.9 .
2.1
15 45
75 225
40 km/hr. 32 km/hr.
43. A can complete a piece of work in 12 days. B
1
1
.
.
50. If
2
x
then
3
x
is equal to
3
x
2
x
is 60% more efficient than A. The number of
days, that B will take to complete the same
work, is
1
.
.
.
1
1 51. If
21.
then the value of
2
x
7
8
2
2
1
.
.
44. Two pipes can fill an empty tank separately
in 24 minutes and 40 minutes respectively
2
.
.
x
.
2 ..
is
x
and a third pipe can empty 30 gallons of
water per minute. If all the three pipes are
open, empty tank becomes full in one hour.
22
22
2
.
.
The capacity of the tank (in gallons) is
800 600
3 .
1..
2..
2..
6..
12.
52. .
1 .
..
1 .
..
1.
..
1.
..
1..
is
500 400
4 .
3..
5..
5..
7..
13.
45.
A batsman, in his 12th innings, makes a score equal to
of 63 runs and thereby increases his average
211 1
score by 2. The average of his score after 12th
1376 5
innings is
41 42
3
(0.13)
3
.
(0.87)
34 35
53.
46. The greatest number, that divides 43, 91 and
183 so as to leave the same remainder in
is equal to
22
(0.87) .
(0.13) .
(0.87) .
(0.13)
1
1
2
each case, is
2
2
54. If x2+ y2- 2x 6y 10 then the value of
(x2 y2) is
7
is equal to
47.
16 6 7 16 67...
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7 .
5 9 7 .
.
11 9.
is
7 .
5 5 .
3
9 .
7 11 .
9
55. The largest among the numbers
56.
If x1/3 y1/3 then y z)3 27 xyz
is equal to
27
57.
If 777 7.... 1
then y is equal to
2
3
43
3
4
58.
If a2 then is equal to
2
a 1
a .
1
a .
1 a .
1
32a
.
a
.
32
59.
The missing term in the sequence
11, ... 17, 19 is
16 15
14 13
60.
The wrong number in the sequence
32 47
63 83
61.
When the price of a toy was increased by
the number of toys sold was decreased
by 15%. What was its effect on the total sales
of the shop?
increase decrease
increase decrease
62.
A person sold a horse at a gain of 15%. Had
he bought it for 25% less and sold it for Rs.
60 less, he would have made a profit of 32%.
The cost price of the horse was
Rs. 370 Rs. 372
Rs. 375 Rs. 378
Solved Paper
63.
A sells an article to B at a gain of 25% B sells
it to C at a gain of 20% and C sells it to D at
a gain of 10%. If D pays Rs. 330 for it, how
much did it cost to A
Rs. 200 Rs. 250
Rs. 275 Rs. 290
64.
By selling an article for Rs. 21, a man lost
such that the percentage loss was equal to
the cost price. The cost priceof the article was
Rs. 30 or Rs. 70 Rs. 35 or Rs. 60
Rs. 45 Rs. 50
65.
Half of 100 articles were sold at a profit of
20% and the rest at a profit of 40%. If all the
articles had been sold at a profit of the
total profit would have been Rs. 100 less
than earlier profit. The cost price of each
article was
Rs. 10 Rs. 15
Rs. 20 Rs. 30
66.
The market price of a clock is Rs. 3200. It is
to be sold at Rs. 2448 at two successive
discounts. If the first discount is then
the second discount is
10%
15% 20%
67.
A dealer marks his goods 30% above his cost
price and then allows 15% discount on it.
What is the cost price of an article on which
he gains Rs. 84
Rs. 800 Rs. 560
Rs. 373.33 Rs. 280
68.
A shopkeeper wishes to give commission
on the marked price of an article but also
wants to earn a profit of 10%. If his cost price
is Rs. 95, then the marked price is
Rs. 100 Rs. 110
Rs. 120 Rs. 130
69.
Krishnamurthy earns Rs. 15000 per month
and spends 80% of it. Due to pay revision,
his monthly income has increased by
but due to price rise, he has to spend 20%
more. His new savings are
Rs. 3400 Rs. 3000
Rs. 4600 Rs. 4000
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1
70.
Two numbers are respectively 12% and
2
25% more than a third number. The first
number is how much per cent of the second
number
90 87.5
25 12.5
71. Population of a town increases 2.5%
annually but is decreased by 0.5% every year
due to migration. What will be the
percentage of increase in 2 years?
4.04
3.96
72.
72% of the students of a certain class took
Biology and 44% took Mathematics. If each
student took at least one of Biology or
Mathematics and 40 students tookboth of
these subjects, the total number of students
in the class is
200 240
250 320
73.
Rs. 1050 are divided among B and C in
2
such a way that the share of A is of the
5
combined share of B and C. A will get
Rs. 200 Rs. 300
Rs. 320 Rs. 420
74.
The sides of a right-angled triangle forming
right angle are in the ratio 5 12. If the area
of the triangle is 270 cm2, then the length of
the hypotenuse is
39cm 42cm
45cm 51cm
75.
Two numbers are in the ratio 5 6. If their
H.C.F is then their L.C.M. will be
90 96
120 150
1
76.
If a b c 1 and ab bc ca then a b
3
c is
2 2
1 1
77.
A and B enter into partnership with capitals
in the ratio 5 6. At the end of 8 months A
withdraws his capital. They recived profits
in the ratio 5 9. Binvested the capital for
6 months 8 months
10 months 12 months
78.
What is the length of the radius of the circumcircle
of the equilateral triangle, the length
ofwhosesideis 63cm
63cm 6cm
5.4cm 36 cm
79.
If the measure of a diagonal and the area of
a rectangle are 25 cm and 168 cm2
respectively, what is the length of the
rectangle
31cm 24cm
17cm 7cm
80.
The number of coins, each of radius 0.75 cm
and thickness 0.2 cm, to be melted to make a
right circular cylinder of height 8 cm and
radius 3 cm, is
640 600 500 480
81.
If the radius of a sphere is increased by 2m,
its surface-area is increased by 704 m2.
What is the radius of the original sphere?
.
22.
.Use ..
.
.
7 .
16m 15m 14 m 13 m
82.
A right circular cylinder is circumscribing a
hemisphere such that their bases are
common. The ratio of their volumes is
1 3 1 2
2 3 3 4
1 1
83. A man invested
3
of his capital at
4
at
and the remaining at 10% rate of simple
interest. If his annualincome from interests
is Rs. 561, the capital invested was
Rs. 6000 Rs. 5600
Rs. 6600 Rs. 7200
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84.
The compound interest on Rs. 6250 at 12%
per annum for 1 year, compounded half-
yearly is
Rs. 772.50 Rs. 772
Rs. 672.50 Rs. 672
85.
A sum of money lent at compound interest
amounts to Rs. 1460 in 2 years and to Rs.
1606 in 3 years.The rate of interest per
annum is
12% 11%
10.5% 10%
86.
If A travels to his school from his house at
the speed of 3 km/hr. then he reaches the
school 5 minutes late. If he travels at the
speed of 4 km/hr, he reaches the school 5
minutes earlier than school time. The
distance of his school from his house is
1km 2km
3 km 4km
87.
A train travelling with a speed of 60 km/hr
catches another train travelling in the same
direction and then leaves it 120 m behind in
18 seconds. The speed of the second train is
26 km/hr 35 km/hr
36 km/hr 63 km/hr
88.
A and B together can complete a piece of
work in 12 days and B and C together in 15
days. If A is twice as good a workman as
then in how many days will be alone
complete the same work
30 25
24 20
89.
4 men and 6 women together can complete
a work in 8 days while 3 men and 7 women
together can complete it in 10 days. 20
women working together will complete it in
36 days 32 days
24 days 20 days
90.
The average of two numbers A and B is 20,
that of B and C is 19 and of C and A it is 21.
What is the value of
24 22
20 18
Solved Paper
Directions The pie chart given below, shows
the expenditure on various items and savings of a
family during the year 2009. Study the pie chart
and answer these questions.
PERCENTAGE OFMONEY SPENT ON VARIOUS
ITEMS AND SAVINGS BYA FAMILYDURING 2009
Others
20%
Savings
15%
Food 23% Clothing
10%
Education
of Children
12%
Transport
Housing
10%
91.
If the total income of the family for the year
2009 was Rs. 1,50,000 then the difference
between the expenditures on housing and
transport was
Rs. 15,000 Rs. 10,000
Rs. 12,000 Rs. 7,500
92.
Maximum expenditure of the family other
than on food, was on
Housing Clothing
Others
Education of children
93.
The savings of the family for the year were
equal to the expenditure on
Food Housing
Education of children
Clothing
94.
The percentage of the income which was
spent on clothing, education of children and
transport together is
17 20
22 27
95.
If the total income of the family was Rs.
1,50,000 then the money spent on food was
Rs. 20,000 Rs. 23,000
Rs. 30,000 Rs. 34,500
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Solved Paper
Directions Study the bar diagram and
ANSWERS
answer these questions.
1. 2. 3. 4. 5.
Persons killed in industrial accident
6. 7. 8. 9. 10.
Persons killed in coal mines
11. 12. 13. 14. 15.
16. 17. 18. 19. 20.
1200
1200
21. 22. 23. 24. 25.
Number of persons
900
800
31. 32. 33. 34. 35.
800
1000
20092008 2007 2006
36. 37. 38. 39. 40.
41. 42. 43. 44. 45.
600
46. 47. 48. 49. 50.
400
300
51. 52. 53. 54. 55.
200
200 56. 57. 58. 59. 60.
200
150
61. 62. 63. 64. 65.
66. 67. 68. 69. 70.
26. 27. 28. 29. 30.
96.
The number of persons killed in coal mines
in 2006 was what per cent of those killed in
industrial accidents in that year
36 300
97.
In which year, minimum number of persons
were killed in industrial accidents and coal
mines together?
2006 2007
2008 2009
98.
In which year, maximum number of persons
were killed in industrial accidents other than
those killed in coal mines?
2006 2007
2008 2009
99.
In which years, minimum number of
persons were killed in coal mines other than
those killed in industrial accidents?
2006 2007
2008 2009
100. In a year, on average, how many persons
were killed in industrial accidents and coal
mines together
121.25 1212
1212.5 1000
4.
71. 72. 73. 74. 75.
76. 77. 78. 79. 80.
81. 82. 83. 84. 85.
86. 87. 88. 89. 90.
91. 92. 93. 94. 95.
96. 97. 98. 99. 100.
EXPLANATIONS
1.
Number of men arranged in the form of a
square
6000 71 5929
.
Number of men arranged in each row
5929 77
2.
4 x Remainder
5 y 2
6 z 3
4
z 6 × 1 4 10
y 5 × 10 3 53
x 4 × 53 2 214
3
(0.75)
2
.
0.75 1
.
..
1
.
0.75
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3 22
(0.75) .(1 .0.75)[(0.75) .0.75 .1.1]
1 0.75
.
.
1 .31 .
1.
x ..3.
xx .
..
..
..
..
x xx
Solved Paper
3 .13
.
3
(0.75) (0.75)
0.25
3
.
.
33
.
3
ab b2) a3- b3] 33
33
0
.
8. If 0.1 1 then, 0.2 2a
1 1 100
4 and 0.02 b then, 0.04 2b
.
1
0.75 0.25 25
.
Expression
..Squareroot= 4 2
a .a .a.b .bb
.
5. x 12 ...(i)
2a .2a .2a.2b .2b .2b
xy= 35 ...(ii)
b
3
a
3
b
3
3
.
.
1
xy 11 .
.
xy yx
12 a
0.125
.
3
3
8
a
3
8b
3
a
.
b
.
35
10. x3 3x2 3x 7
11
6. a2 .b2 .
2 .
2 4 . x3 3x2 3x 1 7 1 8
b
a
1)3 23
x 2
x 1
.
.
.
2
..a2 .1 .b .1
4
22
b
a
2
.
1.2 .
1.2 11. 2x
.
1
.
..
.
.
2
2
b
.
.
b.
4
a
x
.
.
.
.
.
.
a
11
.
.
...(i)
x
.
1.2 .
1.2
x 2
.
.
b .
.
.a
.
.
b.
0
.
.
.
.
a
1
3
x
.
.
3
1
1 x
.
.
b
.
.
0
a
b
a
.
1 .31 .
1 .
x ..3..
xx .
..
..
..
..
a b
x xx
..a2+ b2 1 1 2.
2 ..13 1
.3 .
1
.
.
..
..2
.
2
7.
.x
.
.
x.
3
.
13
.
828 8
1
12
11
.
.
..x
3
x
12. LCM of the orders of the surds LCM of
1 5and7=210
Now, x3
.
3
1
x
1 105
.
.
105
210
5
52 =5210
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Solved Paper
204000
1
1 70
43 4210
.
.
70
210 .
30x 2040000 1800000
4
240000
1
1 42
25 2210
.
.
210
240000
.
x Rs. 8000
30
42
2
1
18. If an article is old to B at profit/loss and
1 30
.
.
30
210
3
B sells the same to C at profit/loss, then
3210
37
C.P.
..The largest number
.
.
100
100
.
.
.
.
.
.
y
x
1
52
.
CP ..
5 .
100 .
.
.
100
13. Expression
.
CP CP
2 23 (13.608) (13.392) .
3 (13.608 13.392)(13.608 13.392) ..
.
100 ..
100 .
.
...
.100 .15 ..100 .10.
100 100
.
.
517.50
Rs. 500
3 27 0.216 .
115 90
19. Let the C.P. of the article be Rs. 100.
2
.
S.P. of the article × 90
3
3 27 216
1000
.
36.
=1.8
.
S.P. of the article
10
903
.
135
2
16. Profit per cent
Trueweight Falseweight
.
False weight
.
100 .
Profit per cent at the original price 35
20. C.P.
.
1000
950
100
.
100
.
45000
Rs. 50000
950
90
100 5 .
S.P.
19 19
110
.
50000
17. If the GP of horse be Rs. then
100
CP of carriage Rs. (20000
Rs. 55000
120 90 .
profit per cent
.
x ..(20000 .x) .
100 100
10000
200
100
.
102 45000 9
.
20000
100 21. C.P. of the article Rs. 100
120x 1800000 90x .
Marked price
.
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Savings 100 13.6 Rs. 86.4
Q Rs. 86.4 100
.
100
100
Rs. 125
80
SP after the discount 100
.
8640
.
Rs. 8640
86.4
.
125
88
.
.
Rs.
..
.
100 .
Rs. 110 Rs. 10000
26. Effect on area .
Gain per cent 10
23. If the marked price of the wrist watch be Rs.
then
10 .
...
10 .
10 10
100 .
.
..
.
90 450
120
.
540
x
Here, nevative sign shows decrease.
100 100
27. Volume of the new ball
.
540
100
.
Rs. 600
34
90 333
..
(rrr ..
123
43
24. Let the original price of tea be Rs. x/kg
23 33)
.
.
.
9x.
8 27)
/kg
New price Rs. ..
.
10 .
36p cubic cm.
22500
22500 4
r3 36.
.
.
.
9
x
3
.
x 25
10
363
.
4
.
r3
27
101
.
9xx
.
.
.
.
22500
.
25
.
.
.
327=3cm
30. 7 years ago, age 4xyears and age
109
.
..
25 5xyears
.
9x.
.
.
22500
.
.
4
14 5
x
.
22500 25 × 9x
.
.
5
14 6
x
22500
.
.
25x 70 24x 84
100
259
.
.
New price
.
present age
.
84- 70 14
9
10
5x 7 5 × 14 7 77 years
100 Rs. 90 per kg.
.
.
11.
25. Let Ram's income Rs. 100. 32. Total profit × .
1 .
..
5000
.
34 .
Donation to charity Rs. 4
Amount deposited in bank 1243
.
....
Total profit × ..
..
5000
12
.
96
10
Rs. 9.6
100 .
Total profit
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.
.
5000
12 2
252
100
Rs. 12000
5
8400
43. Ratio of their efficiency
.
1
.
12000 .
.
share Rs. .
.
.
100: 160= 8
.
3
.
.
Ratio of time taken 8 5
Time taken by B
Rs. 4000
34. Side of the square
515 1
.
12
7
days
121 11 cm
82 2
.
Length of the wire 4 × 11
44. Capacity of the tank x gallons.
44 cm
.
Part of the tank filled in 1 minute
. 2.
r 44
22
x .
x .
30 .
2 ..
r 44 24 40
7
.
xx .
.
r 7 cm
.
.
60
30
.
x
.
.
.
.
24 40
r2
.
Area of circle
.
22
xxx
..
24 40 60
.
77
.
.
30
7
154 sq. cm.
36. If the age edfe of the cube be x cm then,
5x .
3x .
2x
.
30
120
3x 6
x
.
=30 Þ x 600 gallons
6 20
.
23
cm
45. Average of the batsman upto 11th innings
x
3
63 -12 × 2 39
.
Volume of the cube (edge)3
.
Required average 39 2 41
23 .
23 .
23
46. Required number
243 cm3 HCF of (91 (183 91) and (183 43)
37. Required total surface area HCF of 48, 92 and 140 4
r2+4×
r2
47. Expression
.
.
4
r2 sq.unit
.
8
7
39. Difference
22
16 6 7 16 67...
5
..
.
.
r
.
Rs. 10 7
4000
Principal
..
..
..
..
100
100
9 .
7 .
2 .
3 .
7 .
9 .
7 .
2 .
3 .
7
40. Difference Rs. (8652 8400) Rs. 252
7
.
2
Difference
.
100
.
Rate
.
.
.
S.I.
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22
71
.
a .
b .
ab)
3 .
7 .
3 .
72
a2 .
b2 .
ab
48.
Required sum 202 212 ... 292 a b 0.87 0.13 1
(12 22 ... 292) (12 22 ... 192) 54. x2- 2x y2 6y 10 0
x2- 2x y2 6y 9 0
.
29(29 .
.
29 .
19(19 .
.
19 .
.
1)2 3)2 0
.
.
6
6
x 0 .
x 1
.
22 .
n .
nn .
Q1
.
2 .
... .
n .
and, y 0 .
y 3
.
.
.
6 .
x2 y2 9 10
8555 2470
.
..
.
7
7
.
.
5
5
6085 sq.cm.
55.
7
.
5
7 .
5
49.
Expression
9.5 .
0.0085 .
18.9
2
0.0017 .
1.9 .
2.1
7
.
5
225
Similarly,
.
Required square root
2
225= 15
5
21.
.
.
3
.
5
3
1
2
.
.
51. x
2
9
7
9
.
7
.
.
21.
x
2
11
9
11
.
21.
.
9
11
.
x2=
.
21.
2 .
1 21
.
.
Largest number 5
.
3
21.
because its denominator is the smallest.
1 11
1
56.
.
y
3
z3
21.
3
.
x
2
x
Cubing both sides, we have,
1
2
.
.
2
2 .
1 .
21
.
2
x
33
1
1
111 1
.
.
.
.
.
.
x
3 3 3333
.
x
.
..
y ..
3.. y .
x .
y .
z
x
52.
Expression
.
...
..
345313 1 1
....
.
111
4335 7 137
.
x y +3. 333=z
x .
y .
3...
xyz
53. If 0.87 a and 0.13 b then,
111
.
3
b
3
y
.
.
333
3...
xyz
a
Expression
a2 .
b2 .
ab
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Cubing again, 62. If the CP of horse be Rs. x
y z)3 xyz
115
. y z)3 27 xyz 0 then its SP x
100
777 7.... .
3 .
Rs. x
New CP ..
.
4 .
57. Letx
On squaring both sides,
x2= 7x3 115x
.
60
.
.
x2- 7x 0 .
x(x 0
100
.
x 7
3
x
132 99x
7 y 1 73y 3
.
.
.
.
4 100 100
3y 1
115
x
99
3y 4
x
60
.
.
100 100
4
y
.
3 16x
.
60
58. a2 2
100
.
a
2
.
.
60
100
x Rs. 375
16
.
a
21.
From alternative 100 100 100
63. 330 ...
125 120 110
21.
.
1
a
Rs. 200
22
32.
2 .
13 .
.
a 3
64. If the CP of article be Rs. then
22
.
21
x
.
.
100 x3
3 .
22 3 .
22
22
x
x2 100x 2100 0
.
32 .
3 .
4 .
.
1
2 .
x2 70x 30x 2100 0
98.
59. It is sequence of first prime numbers.
.
x 70) 30 70) 0
.
.
30) 70) 0
x Rs. 30 or Rs. 70
60. 8 5 13
13 8 21
21 11 32
65. Let the CP of each article be Rs. x.
32 14 46 .
47
46 17 63 .
5 120
100
x .
.
50 140
100
x .
.
100 125
100
x .
100
61. Effect on sale .
60x 70x 125x 100
20 1520 15
100
..
..
..
..
.
increase
..
5x 100
x
100
5
Rs. 20
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67.
CP of article Rs. .
71. Percentage of increase .
Marked price
.
..
4.04%
.
22.
2 .
2 .
130x 13x
.
100 .
Rs.
100 10
72. Percentage of students opting for both
.
S.P.
subjects
72 44- 100 16
13 85 221x
x
.
Rs.
If thetotal number of studentsbex, then
200
10 100
.
16 4000
221x
x
221
x
40 .
x 250
.
.
x 84 .
84
100
16
200
200
73. 5
.
84
200
.
x =Rs. 800
2
21
..
.
1050
share
Rs. 300
7
68. Marked price Rs. .. then
75. Numbers 5x and 6x
.
.
95 95
110
x
HCF x 4
x Rs. 110
1010
.
100 100
.
LCM 5 × 6 × x
69.
Initial expenditure of Krishnamurthy
5 × 6 × 4 120
80
76. a b c
.
15000
Rs. 12000
100
New income
1
ab bc ca
3
a2+ b2+ c2
.
15000
120
Rs. 18000
100
b c)2 2 (ab bc ca)
New expenditure
21
33
.
1
.
12000
120
Rs. 14400
100
1
.
New savings 18000 14400
Clearly, a b c
3
Rs. 3600
.
a b c 1
Note: It is not an answer choice.
77.
If B invested for y months. then
70.
First number
58.
6
5
25 225
22
.
.
100
y 9
.
y 12 months.
Second number 125
79.
l2 b2 625 ...(i)
.
Required percentage
lb 168 ...(ii)
225
b)2 l2+ b2+ 2lb
100 90
.
.
2
125
625 2 × 168 961
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6250 × 0.1236 Rs. 772.5
l b 961 31 ...(iii)
.
b)2 l2+ b2- 2lb
2
R
.
.
.
.
P1
.
l b 289 17 ...(iv)
3
P1
85. 1460
...(i)
...(ii)
.
.
.
.
625- 168 × 2 289
100
R
.
.
From equations and
1606
.
100.
.
.
2l 48
Dividing equation by
48
.
l =24cm
R 1606
2
.
1
100 1460
r2h
.
80. Volume of the cylinder
× 32 × 8 72.
cm3
R 1606
.
.
1460
.
100 1460
Volume of one coin
× (0.75)2 × 0.2
.
146 1
.
Number of coins
1460 10
72
.
..
0.75 .
0.75 .
0.2
86.
If the distance between the school and home
640
be x km, then
81. 4. 2)2 4.
r2 704
10 x 1
xx
.
34 60
.
12 6
704
. 2)2 r2=
.
4
1
.
12 2 km
.
r2 4r r2
.
x
6
7047
.
4
605
.
87. 60 kmph ..
.
18 .
.
.
56
m/sec
.
22
. 4r 56 4 52
.
r 13 metre 50
m/sec
82.
Required ratio Volume of hemi-sphere 3
Volume of cyliner If the speed of second train be x m/sec, then
2
50
120 20
r3: .
r3= 3
.
.
x
3
3 183
84.
T 2 half years
50
20
.
.
10 m/sec
Rate
x
3
3
.
r 2 .
..
10
.
1.
..
1.
.
18
.
.
CI
P
.
kmph
.
100.
.
.
.
.
..
..
5
36 kmph
..
.
6 .
2
6250 ..
1.
..
1.
89. 8 × 4m 6w × 8
..
100
.
.
.
.
.
10 × 3m 7 × 10w
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.
2m
.
.
22w
94. Required percentage
11w
10 +12 5
.
1m
.
4m+6w=50w
. M1D1 M2D2 95. Expenditure on food
.
50 × 8 20 × D2
.
150000 .
23.
Rs.
508
.
D2= =20days
20
..
..
100
.
Rs. 34500
90.
A B 40
96.
Required percentage
B C 38
300
C+A=42
.
100 25
1200
On adding,
97. Number of persons killed in 2009
120
800 200 1000
.
A B C 60
98.
It is obvious from the bar diagram.
.
A
Required number of the dead 1200
60- 38 22
99.
It is obvious from the bar diagram.
91.
Expenditure on housing and transport
Required number of the dead 150
10
150000
.
100. Required average
100
1500 .
1050 .
1300 .
1000
Rs. 15000
4
92.
It is obvious from the pie chart.
Food .
Others .
20% 4850
1212.5
4
93. Housing
.
15%
Savings .
15%
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SSC
Combined Graduate Level Tier-II Exam
Held on: 01.08.2010
1.
A General, while arranging his men, who
were 6000 in number, in the form of a square,
found that there were 71 men left over. How
many were arranged in each row?
73 77
87 93
2.
A number, when divided successively by
5 and leaves remainders 3 and 4
respectively. The least such number is
50 53
19 214
3.
A number, when divided by 296, gives 75 as
the remainder. If the same number is divided
by 37 then the remainder will be
19 31
4.
The square root of
3
(0.75)
2
..
0.75 .
(0.75) .
1.
.
.
1 .
0.75
5.
The sum and product of two numbers are
12 and 35 respectively. The sum of their
reciprocals will be
11 12 35
35 3512
1
1
6.
If a2 .
b2 ..
then the value of a2+ b2
2
2
a
b
will be
1
1
1 2
2
2
.
1 .
2
7. If .
x ..
then
.
x .
.
1 .
.
x3 .
3 .
is equal to
.
x .
0.1 .
0.1 .
0.1 .
0.02 .
0.02 .
0.02
8.
is equal to
0.2 .
0.2 .
0.2 .
0.04 .
0.04 .
0.04
0.125 0.250
0.500
0.855
1 100 1
9. If x .
then the value of x .
100 is
x
x
10.
If x3+ 3x2+ 3x then x is equal to
36
2
31
11. If 2x .
then the value of x .
3 is
x
x
1311 11 13
.
888 8
12. The greatest number among
357
2,3 is
34 73
5 52
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22
13. 3 (13.608) .
(13.392) is equal to
0.6 0.06
1.8 2.6
.
111 1 .
14.
...
.
... ..
is equal
.
1.
22 .
33 .
4 99 .
100 .
to:
1 99 100 1000
9900 100 99 99
15.
The sum of all the digits of the numbers from
1 to 100 is
5050 903
901 900
16.
A shopkeeper sells suger in such a way that
the selling price of 950g of sugar is the same
as the cost price of 1 kg of sugar. What is his
gain per cent?
51
1
5 4
195
19
17.
A person bought a horse and a carriage for
Rs. 20000. Later, he sold the horse at 20%
profit and the carriage at 10% loss. Thus, he
gained in the whole transaction. The cost
price of the horse was
Rs. 7200 Rs. 7500
Rs. 8000 Rs. 9000
18.
A sells an article to B at 15% profit. B sells it
to C at 10% loss. If C pays Rs. 517.50 for it
then A purchased it at
Rs. 500 Rs. 750
Rs. 1000 Rs. 1250
19.
An article is sold at a certai fixed price. By
2
selling it at of that price, one loses 10%.
3
The gain per cent on selling it at the original
price is
1
20 33
3
200
40
9
20.
A sells an ariticle to B for Rs. 45,000 losing
10% in the transaction. B sells it to C at a
price which would have given a profit of
10% to A. By what per cent does B gain?
75 100 200 150
239 7
21.
The cost price of an article is 80% of its
marked price for sale. How much per cent
does the tradesman gain after allowing a
discount of 12%
20 12
10
22.
A merchant has announced 25% rebate on
prices of ready-made garments at the time
of sale. If a purchase needs to have a rebate
of Rs. 400, then how many shirts, each
costing Rs. 320, should he purchase?
23.
A merchant purchases a wristwatch for Rs.
450 and fixes its list price in a such a way
that after allowing a discount of he
earns a profit of 20%. Then the list price (in
rupees) of the wristwatch is
500 600
750 800
24.
A reduction of 10% in the price of tea enables
a dealer to purchase 25 kg more tea for Rs.
22500. What is the reduced price per kg of
tea?
Rs. 70 Rs. 80
Rs. 90 Rs. 100
25.
Ram donated of his income to a charity
and deposited 10% of the rest in a Bank. If
now he has Rs. 8640 left with him, then his
income is
Rs. 12,500 Rs. 12,000
Rs. 10,500 Rs. 10,000
26.
If the length of a rectangle is increased by
10% and its breadth is decreased by
then its area
decreases by increases by
decreases by
remains unchanged
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27.
Three spherical balls of radius 1 cm, 2 cm
and 3 cm are melted to form a single
spherical ball. In the process, the loss of
material is 25%. The radius of the new ball
is
6cm 5cm
3cm 2cm
28.
IfA C 5andC: D =5:9,then
A D is equal to
11:17 8:27
9 9
29.
If the length of a rectangle is increased in
the ratio 6 7 and its breadth is diminished
in the ratio 5 4 then its area will be
diminished in the ratio
17: 16
8 7
30.
7 years ago, the ages (in years) of A and B
were in the ratio 4 and 7 years hence they
24 36
48 60
32.
C are partners in a business. During a
particular year, A received one third of the
profit, B received one fourth of the profit and
C received the remaining Rs. 5000. How
much amount of money did a receive
Rs. 1000 Rs. 3000
Rs. 4000 Rs. 5000
33.
Three horses are tethered at 3 corners of a
triangular plot of land having sides 20m,
30m and 40m each with a rope of length 7m.
The area (in m2) of the region of this plot,
which can be grazed by the horses, is
.
22.
.Use ..
.
.
7 .
77
75 77 80
3
34.
A wire, when bent in the form of a square,
encloses a region of area 121 cm2. If the same
wire is bent into the form of a circle, then the
area of the circle is
.
..Use ..22
7
.
..
150 cm2 152 cm2
154 cm2 159 cm2
35.
The ratio of the area of a sector of a circle to
the area of the circle is 1 4. If the area of the
circle is 154 cm2, the perimeter of the sector
is
20cm 25cm
36cm 40cm
36.
The length of the diagonal of a cube is 6 cm.
The volume of the cube (in cm3) is
183
283
243
303
will be in the ratio 5 6. The present age of B
is
56 years 63 years
70 years 77 years
37. If a sphere of radius r is divided into four
identical parts, then the total surface area of
31. Two numbers are such that their
the four parts is
difference,their sum and their product are
4
.
r2 square unit (b)2.r2 square unit
in the ratio of 1 7 24. The product of the
numbers is
(c)8.r2 square unit (d)3.r2 square unit
38.
A sum of money, deposited at some rate per
cent per annum of compound interest,
doubles itself in 4 years. In how many years
will it become 16 times of itself at the same
rate
16 12
10
39.
What is the difference between the
compound interest and simple interest on
Rs. 4000 at per annum for 2 years
10 11
20 100
40.
The simple and compound interests on a
sum of money for 2 year are Rs. 8400 and
Rs. 8652 respectively. The rate of interest per
annum is
7.5% 4.5%
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41.
A man can row against the current three-
fourth of a kilometre in 15 minutes and
returns the same distance in 10 minutes. The
ratio of his speed to that of the current is
5 3
5 1
42.
Two places A and B are 100 km apart on a
highway.One car startsfromAandanother
from B at the same time. If the cars travel in
the same direction at a constant speed, they
meet in 5 hours. If the cars travel towards
each other, they meet in 1 hour. What is the
speed of the car running faster
60 km/hr. 50 km/hr.
111 1
234 5
48.
The sum of the areas of the 10 squares, the
lengths of whose sides are 20 cm, 21 cm, ....
29 cm respectively is
6085 cm2 8555 cm2
2470 cm2 11025 cm2
49.
The square root of
9.5 .
0.0085 .
18.9
is
0.0017 .
1.9 .
2.1
15 45
75 225
40 km/hr. 32 km/hr.
43. A can complete a piece of work in 12 days. B
1
1
.
.
50. If
2
x
then
3
x
is equal to
3
x
2
x
is 60% more efficient than A. The number of
days, that B will take to complete the same
work, is
1
.
.
.
1
1 51. If
21.
then the value of
2
x
7
8
2
2
1
.
.
44. Two pipes can fill an empty tank separately
in 24 minutes and 40 minutes respectively
2
.
.
x
.
2 ..
is
x
and a third pipe can empty 30 gallons of
water per minute. If all the three pipes are
open, empty tank becomes full in one hour.
22
22
2
.
.
The capacity of the tank (in gallons) is
800 600
3 .
1..
2..
2..
6..
12.
52. .
1 .
..
1 .
..
1.
..
1.
..
1..
is
500 400
4 .
3..
5..
5..
7..
13.
45.
A batsman, in his 12th innings, makes a score equal to
of 63 runs and thereby increases his average
211 1
score by 2. The average of his score after 12th
1376 5
innings is
41 42
3
(0.13)
3
.
(0.87)
34 35
53.
46. The greatest number, that divides 43, 91 and
183 so as to leave the same remainder in
is equal to
22
(0.87) .
(0.13) .
(0.87) .
(0.13)
1
1
2
each case, is
2
2
54. If x2+ y2- 2x 6y 10 then the value of
(x2 y2) is
7
is equal to
47.
16 6 7 16 67...
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7 .
5 9 7 .
.
11 9.
is
7 .
5 5 .
3
9 .
7 11 .
9
55. The largest among the numbers
56.
If x1/3 y1/3 then y z)3 27 xyz
is equal to
27
57.
If 777 7.... 1
then y is equal to
2
3
43
3
4
58.
If a2 then is equal to
2
a 1
a .
1
a .
1 a .
1
32a
.
a
.
32
59.
The missing term in the sequence
11, ... 17, 19 is
16 15
14 13
60.
The wrong number in the sequence
32 47
63 83
61.
When the price of a toy was increased by
the number of toys sold was decreased
by 15%. What was its effect on the total sales
of the shop?
increase decrease
increase decrease
62.
A person sold a horse at a gain of 15%. Had
he bought it for 25% less and sold it for Rs.
60 less, he would have made a profit of 32%.
The cost price of the horse was
Rs. 370 Rs. 372
Rs. 375 Rs. 378
Solved Paper
63.
A sells an article to B at a gain of 25% B sells
it to C at a gain of 20% and C sells it to D at
a gain of 10%. If D pays Rs. 330 for it, how
much did it cost to A
Rs. 200 Rs. 250
Rs. 275 Rs. 290
64.
By selling an article for Rs. 21, a man lost
such that the percentage loss was equal to
the cost price. The cost priceof the article was
Rs. 30 or Rs. 70 Rs. 35 or Rs. 60
Rs. 45 Rs. 50
65.
Half of 100 articles were sold at a profit of
20% and the rest at a profit of 40%. If all the
articles had been sold at a profit of the
total profit would have been Rs. 100 less
than earlier profit. The cost price of each
article was
Rs. 10 Rs. 15
Rs. 20 Rs. 30
66.
The market price of a clock is Rs. 3200. It is
to be sold at Rs. 2448 at two successive
discounts. If the first discount is then
the second discount is
10%
15% 20%
67.
A dealer marks his goods 30% above his cost
price and then allows 15% discount on it.
What is the cost price of an article on which
he gains Rs. 84
Rs. 800 Rs. 560
Rs. 373.33 Rs. 280
68.
A shopkeeper wishes to give commission
on the marked price of an article but also
wants to earn a profit of 10%. If his cost price
is Rs. 95, then the marked price is
Rs. 100 Rs. 110
Rs. 120 Rs. 130
69.
Krishnamurthy earns Rs. 15000 per month
and spends 80% of it. Due to pay revision,
his monthly income has increased by
but due to price rise, he has to spend 20%
more. His new savings are
Rs. 3400 Rs. 3000
Rs. 4600 Rs. 4000
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1
70.
Two numbers are respectively 12% and
2
25% more than a third number. The first
number is how much per cent of the second
number
90 87.5
25 12.5
71. Population of a town increases 2.5%
annually but is decreased by 0.5% every year
due to migration. What will be the
percentage of increase in 2 years?
4.04
3.96
72.
72% of the students of a certain class took
Biology and 44% took Mathematics. If each
student took at least one of Biology or
Mathematics and 40 students tookboth of
these subjects, the total number of students
in the class is
200 240
250 320
73.
Rs. 1050 are divided among B and C in
2
such a way that the share of A is of the
5
combined share of B and C. A will get
Rs. 200 Rs. 300
Rs. 320 Rs. 420
74.
The sides of a right-angled triangle forming
right angle are in the ratio 5 12. If the area
of the triangle is 270 cm2, then the length of
the hypotenuse is
39cm 42cm
45cm 51cm
75.
Two numbers are in the ratio 5 6. If their
H.C.F is then their L.C.M. will be
90 96
120 150
1
76.
If a b c 1 and ab bc ca then a b
3
c is
2 2
1 1
77.
A and B enter into partnership with capitals
in the ratio 5 6. At the end of 8 months A
withdraws his capital. They recived profits
in the ratio 5 9. Binvested the capital for
6 months 8 months
10 months 12 months
78.
What is the length of the radius of the circumcircle
of the equilateral triangle, the length
ofwhosesideis 63cm
63cm 6cm
5.4cm 36 cm
79.
If the measure of a diagonal and the area of
a rectangle are 25 cm and 168 cm2
respectively, what is the length of the
rectangle
31cm 24cm
17cm 7cm
80.
The number of coins, each of radius 0.75 cm
and thickness 0.2 cm, to be melted to make a
right circular cylinder of height 8 cm and
radius 3 cm, is
640 600 500 480
81.
If the radius of a sphere is increased by 2m,
its surface-area is increased by 704 m2.
What is the radius of the original sphere?
.
22.
.Use ..
.
.
7 .
16m 15m 14 m 13 m
82.
A right circular cylinder is circumscribing a
hemisphere such that their bases are
common. The ratio of their volumes is
1 3 1 2
2 3 3 4
1 1
83. A man invested
3
of his capital at
4
at
and the remaining at 10% rate of simple
interest. If his annualincome from interests
is Rs. 561, the capital invested was
Rs. 6000 Rs. 5600
Rs. 6600 Rs. 7200
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84.
The compound interest on Rs. 6250 at 12%
per annum for 1 year, compounded half-
yearly is
Rs. 772.50 Rs. 772
Rs. 672.50 Rs. 672
85.
A sum of money lent at compound interest
amounts to Rs. 1460 in 2 years and to Rs.
1606 in 3 years.The rate of interest per
annum is
12% 11%
10.5% 10%
86.
If A travels to his school from his house at
the speed of 3 km/hr. then he reaches the
school 5 minutes late. If he travels at the
speed of 4 km/hr, he reaches the school 5
minutes earlier than school time. The
distance of his school from his house is
1km 2km
3 km 4km
87.
A train travelling with a speed of 60 km/hr
catches another train travelling in the same
direction and then leaves it 120 m behind in
18 seconds. The speed of the second train is
26 km/hr 35 km/hr
36 km/hr 63 km/hr
88.
A and B together can complete a piece of
work in 12 days and B and C together in 15
days. If A is twice as good a workman as
then in how many days will be alone
complete the same work
30 25
24 20
89.
4 men and 6 women together can complete
a work in 8 days while 3 men and 7 women
together can complete it in 10 days. 20
women working together will complete it in
36 days 32 days
24 days 20 days
90.
The average of two numbers A and B is 20,
that of B and C is 19 and of C and A it is 21.
What is the value of
24 22
20 18
Solved Paper
Directions The pie chart given below, shows
the expenditure on various items and savings of a
family during the year 2009. Study the pie chart
and answer these questions.
PERCENTAGE OFMONEY SPENT ON VARIOUS
ITEMS AND SAVINGS BYA FAMILYDURING 2009
Others
20%
Savings
15%
Food 23% Clothing
10%
Education
of Children
12%
Transport
Housing
10%
91.
If the total income of the family for the year
2009 was Rs. 1,50,000 then the difference
between the expenditures on housing and
transport was
Rs. 15,000 Rs. 10,000
Rs. 12,000 Rs. 7,500
92.
Maximum expenditure of the family other
than on food, was on
Housing Clothing
Others
Education of children
93.
The savings of the family for the year were
equal to the expenditure on
Food Housing
Education of children
Clothing
94.
The percentage of the income which was
spent on clothing, education of children and
transport together is
17 20
22 27
95.
If the total income of the family was Rs.
1,50,000 then the money spent on food was
Rs. 20,000 Rs. 23,000
Rs. 30,000 Rs. 34,500
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Solved Paper
Directions Study the bar diagram and
ANSWERS
answer these questions.
1. 2. 3. 4. 5.
Persons killed in industrial accident
6. 7. 8. 9. 10.
Persons killed in coal mines
11. 12. 13. 14. 15.
16. 17. 18. 19. 20.
1200
1200
21. 22. 23. 24. 25.
Number of persons
900
800
31. 32. 33. 34. 35.
800
1000
20092008 2007 2006
36. 37. 38. 39. 40.
41. 42. 43. 44. 45.
600
46. 47. 48. 49. 50.
400
300
51. 52. 53. 54. 55.
200
200 56. 57. 58. 59. 60.
200
150
61. 62. 63. 64. 65.
66. 67. 68. 69. 70.
26. 27. 28. 29. 30.
96.
The number of persons killed in coal mines
in 2006 was what per cent of those killed in
industrial accidents in that year
36 300
97.
In which year, minimum number of persons
were killed in industrial accidents and coal
mines together?
2006 2007
2008 2009
98.
In which year, maximum number of persons
were killed in industrial accidents other than
those killed in coal mines?
2006 2007
2008 2009
99.
In which years, minimum number of
persons were killed in coal mines other than
those killed in industrial accidents?
2006 2007
2008 2009
100. In a year, on average, how many persons
were killed in industrial accidents and coal
mines together
121.25 1212
1212.5 1000
4.
71. 72. 73. 74. 75.
76. 77. 78. 79. 80.
81. 82. 83. 84. 85.
86. 87. 88. 89. 90.
91. 92. 93. 94. 95.
96. 97. 98. 99. 100.
EXPLANATIONS
1.
Number of men arranged in the form of a
square
6000 71 5929
.
Number of men arranged in each row
5929 77
2.
4 x Remainder
5 y 2
6 z 3
4
z 6 × 1 4 10
y 5 × 10 3 53
x 4 × 53 2 214
3
(0.75)
2
.
0.75 1
.
..
1
.
0.75
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3 22
(0.75) .(1 .0.75)[(0.75) .0.75 .1.1]
1 0.75
.
.
1 .31 .
1.
x ..3.
xx .
..
..
..
..
x xx
Solved Paper
3 .13
.
3
(0.75) (0.75)
0.25
3
.
.
33
.
3
ab b2) a3- b3] 33
33
0
.
8. If 0.1 1 then, 0.2 2a
1 1 100
4 and 0.02 b then, 0.04 2b
.
1
0.75 0.25 25
.
Expression
..Squareroot= 4 2
a .a .a.b .bb
.
5. x 12 ...(i)
2a .2a .2a.2b .2b .2b
xy= 35 ...(ii)
b
3
a
3
b
3
3
.
.
1
xy 11 .
.
xy yx
12 a
0.125
.
3
3
8
a
3
8b
3
a
.
b
.
35
10. x3 3x2 3x 7
11
6. a2 .b2 .
2 .
2 4 . x3 3x2 3x 1 7 1 8
b
a
1)3 23
x 2
x 1
.
.
.
2
..a2 .1 .b .1
4
22
b
a
2
.
1.2 .
1.2 11. 2x
.
1
.
..
.
.
2
2
b
.
.
b.
4
a
x
.
.
.
.
.
.
a
11
.
.
...(i)
x
.
1.2 .
1.2
x 2
.
.
b .
.
.a
.
.
b.
0
.
.
.
.
a
1
3
x
.
.
3
1
1 x
.
.
b
.
.
0
a
b
a
.
1 .31 .
1 .
x ..3..
xx .
..
..
..
..
a b
x xx
..a2+ b2 1 1 2.
2 ..13 1
.3 .
1
.
.
..
..2
.
2
7.
.x
.
.
x.
3
.
13
.
828 8
1
12
11
.
.
..x
3
x
12. LCM of the orders of the surds LCM of
1 5and7=210
Now, x3
.
3
1
x
1 105
.
.
105
210
5
52 =5210
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204000
1
1 70
43 4210
.
.
70
210 .
30x 2040000 1800000
4
240000
1
1 42
25 2210
.
.
210
240000
.
x Rs. 8000
30
42
2
1
18. If an article is old to B at profit/loss and
1 30
.
.
30
210
3
B sells the same to C at profit/loss, then
3210
37
C.P.
..The largest number
.
.
100
100
.
.
.
.
.
.
y
x
1
52
.
CP ..
5 .
100 .
.
.
100
13. Expression
.
CP CP
2 23 (13.608) (13.392) .
3 (13.608 13.392)(13.608 13.392) ..
.
100 ..
100 .
.
...
.100 .15 ..100 .10.
100 100
.
.
517.50
Rs. 500
3 27 0.216 .
115 90
19. Let the C.P. of the article be Rs. 100.
2
.
S.P. of the article × 90
3
3 27 216
1000
.
36.
=1.8
.
S.P. of the article
10
903
.
135
2
16. Profit per cent
Trueweight Falseweight
.
False weight
.
100 .
Profit per cent at the original price 35
20. C.P.
.
1000
950
100
.
100
.
45000
Rs. 50000
950
90
100 5 .
S.P.
19 19
110
.
50000
17. If the GP of horse be Rs. then
100
CP of carriage Rs. (20000
Rs. 55000
120 90 .
profit per cent
.
x ..(20000 .x) .
100 100
10000
200
100
.
102 45000 9
.
20000
100 21. C.P. of the article Rs. 100
120x 1800000 90x .
Marked price
.
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Solved Paper
Savings 100 13.6 Rs. 86.4
Q Rs. 86.4 100
.
100
100
Rs. 125
80
SP after the discount 100
.
8640
.
Rs. 8640
86.4
.
125
88
.
.
Rs.
..
.
100 .
Rs. 110 Rs. 10000
26. Effect on area .
Gain per cent 10
23. If the marked price of the wrist watch be Rs.
then
10 .
...
10 .
10 10
100 .
.
..
.
90 450
120
.
540
x
Here, nevative sign shows decrease.
100 100
27. Volume of the new ball
.
540
100
.
Rs. 600
34
90 333
..
(rrr ..
123
43
24. Let the original price of tea be Rs. x/kg
23 33)
.
.
.
9x.
8 27)
/kg
New price Rs. ..
.
10 .
36p cubic cm.
22500
22500 4
r3 36.
.
.
.
9
x
3
.
x 25
10
363
.
4
.
r3
27
101
.
9xx
.
.
.
.
22500
.
25
.
.
.
327=3cm
30. 7 years ago, age 4xyears and age
109
.
..
25 5xyears
.
9x.
.
.
22500
.
.
4
14 5
x
.
22500 25 × 9x
.
.
5
14 6
x
22500
.
.
25x 70 24x 84
100
259
.
.
New price
.
present age
.
84- 70 14
9
10
5x 7 5 × 14 7 77 years
100 Rs. 90 per kg.
.
.
11.
25. Let Ram's income Rs. 100. 32. Total profit × .
1 .
..
5000
.
34 .
Donation to charity Rs. 4
Amount deposited in bank 1243
.
....
Total profit × ..
..
5000
12
.
96
10
Rs. 9.6
100 .
Total profit
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Solved Paper
.
.
5000
12 2
252
100
Rs. 12000
5
8400
43. Ratio of their efficiency
.
1
.
12000 .
.
share Rs. .
.
.
100: 160= 8
.
3
.
.
Ratio of time taken 8 5
Time taken by B
Rs. 4000
34. Side of the square
515 1
.
12
7
days
121 11 cm
82 2
.
Length of the wire 4 × 11
44. Capacity of the tank x gallons.
44 cm
.
Part of the tank filled in 1 minute
. 2.
r 44
22
x .
x .
30 .
2 ..
r 44 24 40
7
.
xx .
.
r 7 cm
.
.
60
30
.
x
.
.
.
.
24 40
r2
.
Area of circle
.
22
xxx
..
24 40 60
.
77
.
.
30
7
154 sq. cm.
36. If the age edfe of the cube be x cm then,
5x .
3x .
2x
.
30
120
3x 6
x
.
=30 Þ x 600 gallons
6 20
.
23
cm
45. Average of the batsman upto 11th innings
x
3
63 -12 × 2 39
.
Volume of the cube (edge)3
.
Required average 39 2 41
23 .
23 .
23
46. Required number
243 cm3 HCF of (91 (183 91) and (183 43)
37. Required total surface area HCF of 48, 92 and 140 4
r2+4×
r2
47. Expression
.
.
4
r2 sq.unit
.
8
7
39. Difference
22
16 6 7 16 67...
5
..
.
.
r
.
Rs. 10 7
4000
Principal
..
..
..
..
100
100
9 .
7 .
2 .
3 .
7 .
9 .
7 .
2 .
3 .
7
40. Difference Rs. (8652 8400) Rs. 252
7
.
2
Difference
.
100
.
Rate
.
.
.
S.I.
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Solved Paper
22
71
.
a .
b .
ab)
3 .
7 .
3 .
72
a2 .
b2 .
ab
48.
Required sum 202 212 ... 292 a b 0.87 0.13 1
(12 22 ... 292) (12 22 ... 192) 54. x2- 2x y2 6y 10 0
x2- 2x y2 6y 9 0
.
29(29 .
.
29 .
19(19 .
.
19 .
.
1)2 3)2 0
.
.
6
6
x 0 .
x 1
.
22 .
n .
nn .
Q1
.
2 .
... .
n .
and, y 0 .
y 3
.
.
.
6 .
x2 y2 9 10
8555 2470
.
..
.
7
7
.
.
5
5
6085 sq.cm.
55.
7
.
5
7 .
5
49.
Expression
9.5 .
0.0085 .
18.9
2
0.0017 .
1.9 .
2.1
7
.
5
225
Similarly,
.
Required square root
2
225= 15
5
21.
.
.
3
.
5
3
1
2
.
.
51. x
2
9
7
9
.
7
.
.
21.
x
2
11
9
11
.
21.
.
9
11
.
x2=
.
21.
2 .
1 21
.
.
Largest number 5
.
3
21.
because its denominator is the smallest.
1 11
1
56.
.
y
3
z3
21.
3
.
x
2
x
Cubing both sides, we have,
1
2
.
.
2
2 .
1 .
21
.
2
x
33
1
1
111 1
.
.
.
.
.
.
x
3 3 3333
.
x
.
..
y ..
3.. y .
x .
y .
z
x
52.
Expression
.
...
..
345313 1 1
....
.
111
4335 7 137
.
x y +3. 333=z
x .
y .
3...
xyz
53. If 0.87 a and 0.13 b then,
111
.
3
b
3
y
.
.
333
3...
xyz
a
Expression
a2 .
b2 .
ab
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Solved Paper
Cubing again, 62. If the CP of horse be Rs. x
y z)3 xyz
115
. y z)3 27 xyz 0 then its SP x
100
777 7.... .
3 .
Rs. x
New CP ..
.
4 .
57. Letx
On squaring both sides,
x2= 7x3 115x
.
60
.
.
x2- 7x 0 .
x(x 0
100
.
x 7
3
x
132 99x
7 y 1 73y 3
.
.
.
.
4 100 100
3y 1
115
x
99
3y 4
x
60
.
.
100 100
4
y
.
3 16x
.
60
58. a2 2
100
.
a
2
.
.
60
100
x Rs. 375
16
.
a
21.
From alternative 100 100 100
63. 330 ...
125 120 110
21.
.
1
a
Rs. 200
22
32.
2 .
13 .
.
a 3
64. If the CP of article be Rs. then
22
.
21
x
.
.
100 x3
3 .
22 3 .
22
22
x
x2 100x 2100 0
.
32 .
3 .
4 .
.
1
2 .
x2 70x 30x 2100 0
98.
59. It is sequence of first prime numbers.
.
x 70) 30 70) 0
.
.
30) 70) 0
x Rs. 30 or Rs. 70
60. 8 5 13
13 8 21
21 11 32
65. Let the CP of each article be Rs. x.
32 14 46 .
47
46 17 63 .
5 120
100
x .
.
50 140
100
x .
.
100 125
100
x .
100
61. Effect on sale .
60x 70x 125x 100
20 1520 15
100
..
..
..
..
.
increase
..
5x 100
x
100
5
Rs. 20
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67.
CP of article Rs. .
71. Percentage of increase .
Marked price
.
..
4.04%
.
22.
2 .
2 .
130x 13x
.
100 .
Rs.
100 10
72. Percentage of students opting for both
.
S.P.
subjects
72 44- 100 16
13 85 221x
x
.
Rs.
If thetotal number of studentsbex, then
200
10 100
.
16 4000
221x
x
221
x
40 .
x 250
.
.
x 84 .
84
100
16
200
200
73. 5
.
84
200
.
x =Rs. 800
2
21
..
.
1050
share
Rs. 300
7
68. Marked price Rs. .. then
75. Numbers 5x and 6x
.
.
95 95
110
x
HCF x 4
x Rs. 110
1010
.
100 100
.
LCM 5 × 6 × x
69.
Initial expenditure of Krishnamurthy
5 × 6 × 4 120
80
76. a b c
.
15000
Rs. 12000
100
New income
1
ab bc ca
3
a2+ b2+ c2
.
15000
120
Rs. 18000
100
b c)2 2 (ab bc ca)
New expenditure
21
33
.
1
.
12000
120
Rs. 14400
100
1
.
New savings 18000 14400
Clearly, a b c
3
Rs. 3600
.
a b c 1
Note: It is not an answer choice.
77.
If B invested for y months. then
70.
First number
58.
6
5
25 225
22
.
.
100
y 9
.
y 12 months.
Second number 125
79.
l2 b2 625 ...(i)
.
Required percentage
lb 168 ...(ii)
225
b)2 l2+ b2+ 2lb
100 90
.
.
2
125
625 2 × 168 961
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6250 × 0.1236 Rs. 772.5
l b 961 31 ...(iii)
.
b)2 l2+ b2- 2lb
2
R
.
.
.
.
P1
.
l b 289 17 ...(iv)
3
P1
85. 1460
...(i)
...(ii)
.
.
.
.
625- 168 × 2 289
100
R
.
.
From equations and
1606
.
100.
.
.
2l 48
Dividing equation by
48
.
l =24cm
R 1606
2
.
1
100 1460
r2h
.
80. Volume of the cylinder
× 32 × 8 72.
cm3
R 1606
.
.
1460
.
100 1460
Volume of one coin
× (0.75)2 × 0.2
.
146 1
.
Number of coins
1460 10
72
.
..
0.75 .
0.75 .
0.2
86.
If the distance between the school and home
640
be x km, then
81. 4. 2)2 4.
r2 704
10 x 1
xx
.
34 60
.
12 6
704
. 2)2 r2=
.
4
1
.
12 2 km
.
r2 4r r2
.
x
6
7047
.
4
605
.
87. 60 kmph ..
.
18 .
.
.
56
m/sec
.
22
. 4r 56 4 52
.
r 13 metre 50
m/sec
82.
Required ratio Volume of hemi-sphere 3
Volume of cyliner If the speed of second train be x m/sec, then
2
50
120 20
r3: .
r3= 3
.
.
x
3
3 183
84.
T 2 half years
50
20
.
.
10 m/sec
Rate
x
3
3
.
r 2 .
..
10
.
1.
..
1.
.
18
.
.
CI
P
.
kmph
.
100.
.
.
.
.
..
..
5
36 kmph
..
.
6 .
2
6250 ..
1.
..
1.
89. 8 × 4m 6w × 8
..
100
.
.
.
.
.
10 × 3m 7 × 10w
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.
2m
.
.
22w
94. Required percentage
11w
10 +12 5
.
1m
.
4m+6w=50w
. M1D1 M2D2 95. Expenditure on food
.
50 × 8 20 × D2
.
150000 .
23.
Rs.
508
.
D2= =20days
20
..
..
100
.
Rs. 34500
90.
A B 40
96.
Required percentage
B C 38
300
C+A=42
.
100 25
1200
On adding,
97. Number of persons killed in 2009
120
800 200 1000
.
A B C 60
98.
It is obvious from the bar diagram.
.
A
Required number of the dead 1200
60- 38 22
99.
It is obvious from the bar diagram.
91.
Expenditure on housing and transport
Required number of the dead 150
10
150000
.
100. Required average
100
1500 .
1050 .
1300 .
1000
Rs. 15000
4
92.
It is obvious from the pie chart.
Food .
Others .
20% 4850
1212.5
4
93. Housing
.
15%
Savings .
15%
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