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-SSC TIER-II
HELD 16-09-2012

PAPER I
QUANTITATIVE ABILITIES


1 . There are 200 questions on a 3 hour examination. Among 200 questions, 50 are
Science. He spent twice, as much time on each Mathematics questions as for each
other question. How many minutes did he spend on Mathematics questions?
100 60 36 72
2 . The remainder when 919 6 is divided 8 is
7 2 3
3 . The least five-digit perfect square number which id divisible by and 8 is
10 800 10 201 14 400 32 400
4 . Which of the following numbers does not fit into the series?
14, 19, 29, 40, 44, 51, 59, 73
44 29 59 51
5 . What will be the remainder when 19100 is divided by 20?
1 19 20
6 . A toy factory manufactured a batch of electronic toys. If the toys were packed in
boxes of 115 each, 13 boxes would not be filled completely. If the boys were packed
in boxes of 65 each, 22 such boxes would not be enough to pack all of them.
Coincidentally, in the end, the toys were packed n in boxes containing n toys each,
without any remainder. The total number of toys was
1 444 1 454 1 424 1 434
7. 3 0.000729
0.085184
44 27 27 9


9 42 44 44

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8 . Complete the series:
26, 63, 124, 215, 342,
391 421 481 5 11
9 . A woman sells to the first customer half her stock of apples and half an apple, to the
second customer half an apple and half of her remaining stock and so also to a
third and to a fourth customer. She finds that she has now 15 apples left. How
many had she at first?
125 255 250 155
10 . A and B can complete a job in 24 days 1 working together. A alone can complete it
in 32 days. Both of them worked together for 8 days and them A left. The number of
days B will take to complete the remaining job is
64 128 16 32
11.
In a factory, there are equal number of women and children. Women work for 6
hours a day an children and 4 hours a day. During festival time, the work load goes
up by 50%. The government rule does not allow children to work for more than 6
hours a day. If they are equally efficient and the extra work is done by women, then
extra hours of work put in by women every day are
9 5 3
12 . A and B each working alone can do a work in 15 days and 25 days respectively.
They started the work together, but B left after some time and A finished the
remaining work in 7 days. After how many days from the start did B leave?
9 3 5
13 . A and B started a business with Rs. 20,000 and Rs. 35,000 respectively. They agreed
to share the profit in the ratio of their capital C joins the partnership with the
condition and lays Rs. 2,20,000 as premium for this, be shared between A and B.
This is to divided between A and B in the ratio of
9 10 10 9 10 1 1 10
14 . A can complete a work in 20 days and B 30 days. A worked alone for 4 days and the
B completed the remaining work along with C in 18 days. In how many days can
working alone complete the work?
72 90
12 68
15 . A pipe can fill a cistern in 12 minutes and another pipe can fill it in 15 minutes, but
third pipe can empty it in 6 minutes. The first two pipes are kept open for 5 minutes
in the beginning and then the third pipe also opened. Number of minutes taken
empty the cistern is
42 45
38 22
16 . Brothers A and B had some savings in the ratio 4 5. They decided to buy a gift for
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their sister, sharing the cost in the ratio 3 4. After they bought, A spent two-third of
his amount while B is left with Rs. 145. Them the value of the fit is

Rs. 140 Rs. 175 Rs. 70 Rs. 105
17 . The taxi charges in a city contain fixed charges and additional charge.km.
The
fixed charge is for a distance of upto 5 km and additional charge/km thereafter.
The charge for a distance of 10 km is Rs. 350 and for 25 km is Rs. 800. The charge
for a distance of 30 km is
Rs. 900 Rs. 950 Rs. 800 Rs. 750
18 . The marks of 3 students B and C are in the ratio 10 12 15. If the maximum
marks of the paper are 100, then the marks of B cannot be in the range of
70 80 80 90 20 30 40 50
19 . The average of the test scores of a class of students is 70 and that of students
is 91. When the scores of both the classes are combined, the average is 80. What is

10/13 10/11 11/10 13/10
20 . The average salary per head of all workers of an institution is Rs. 60. The average
salary per head of 12 officers is Rs. 400. The average salary per head of the rest is
Rs. 56. Then the total number of workers in the institution is
1 062 1 060 1 030 1 032
21 . A cricketer played 80 innings and scored an average of 99 runs. His score is in the
last inning is zero run. To have an average of 100 at the end, his score in the last
innings should have been
60 runs 80 runs 10 runs 1 run
22 . A man spends an average of Rs. 1,694.70 per month for the first 7 months and
Rs.1,810.50 per month for the next 5 months. His monthly salary if he saves Rs.
3,084.60 during the whole year is
Rs. 1,000 Rs. 2,000 Rs. 2,400 Rs. 3,000
23 . A and B undertake to do a piece of work for Rs. 2,200. A alone can do it in 8 days,
while B can do it in 6 days. With the help of they complete it in 3 days. Find
share.
Rs. 150 Rs. 100 Rs. 450 Rs. 300
24 . By selling an article at 80% of it marked price, a trader makes a loss of 10%. What
will be the profit percentage if he sells it at 95% of its marked price?
5.9 12 .5 6.9 5
25 . By selling an umbrella for Rs. 30, a shopkeeper gains 20%. During a clearance sale,
the shopkeeper allows a discount of 10% of the marked price. He gain during eh
sale season is
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9 7 7.5

26 . What is the maximum percentage discount (approximately) that a merchant can
offer on his marked price so that he ends up selling at no profit or loss, if he initially
marked his goods up by
33. 28. 60% No discount
27 . A shopkeeper marks the prices at 15% higher than the original price. Due to increase
in demand, he further increase the price by 10%. How much percentage profit will
he get?
20 24 .5 25 26 .5
28 . From a vessel containing 100 l of wine, 10 l are drawn out and an equal amount of
water is added. From the mixture, 10 l is again drawn out and same quantity of
water is added. What is the final ratio of wine and water?
91 9 81 19 80 20 90 10
29 . From each of two given numbers, half the smaller number is subtracted. After such
subtraction, the larger number is 4 times as large as the smaller number. What is the
ratio of the numbers?
4 1 4 5 5 2 1 4
30 . Men, women and children are employed to do a work in the proportion of 3 2 1
and their wages as 5 3 :2. When 90 men are employed, total daily wages of all
amounts to Rs. 10,350. Find the daily wage of a man.
Rs. 115 Rs. 75 Rs. 45 Rs. 57.50
1

31 . A sells an article to B making a profit of of his outlay. B sells it to gaining 20%.
5
1

If C sells it for Rs. 600 and incurs a loss of of his outlay, the cost price of A is

6

Rs. 720 Rs. 800 Rs. 600 Rs. 500
32 . A man had a certain amount with him. He spent 20% of that to buy an article and
of the remaining on transport. Then he gifted Rs. 120. If he is left with Rs. 1,400,
the amount he spent on transport is
Rs. 95 Rs.80 Rs. 76 Rs. 61
33 . The population of a town is 3,11,250. The ratio between women and men is 43 40.
If there are 24% literate among men and literature among women, the total
number of literature persons in the town is
56, 800 99, 600 41, 800 48, 900
34 . In an examination, 52% of the candidates failed in English and 43% failed in
Mathematics. If 17% failed in both the subjects, then the percentage of candidates,
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who passed in both the subjects, was

25 22
23 21
35 . In a election there were only two candidates. One of the candidates secured 40% of
votes and is defined by the other candidate by 298 votes. The total number of votes
polled is
1 490 1 500 745 1 460
36 . P and Q are 27 km away.
Two trains with speeds of 24 km/hr and 18 km/hr
respectively start simultaneously from P and Q and travel in the same direction.
They meet at a point R beyond Q. Distance QR is
48 km 36 km 126 km 81 km
37 . A boat covers 12 km upstream in 3 hours, while it covers 36 km upstream and 24
1

km downstream in 6 hours. What is the speed of the current?

2

2 km/hr 2.5 km/hr 1.5 km/hr 1 km/hr
38 . Average rainfall on Monday, Tuesday, Wednesday and Thursday is 420.5 cm and
average on Tuesday, Wednesday, Thursday and Friday is 330.5 cm. If the ratio of
rainfall for Monday and Friday is 20 21, find the rainfall in cm on Monday and
Friday.
1700, 1740 1682, 1762 1800, 1890 1600, 1680
39 . The average of 5 consecutive integers starting with is n. What is the average of
6 consecutive integers starting with
2 9 n
2 5

n



2
2

40 . A manufacture sells an article to a wholesale dealer at a profit of 10%. The wholesale
dealer sells it to a shopkeeper at 20% profit. The shopkeeper sells it to a customer for
Rs. 56,100 at a loss of 15%. Then the cost price of the article to the manufacture is
Rs. 50,000 Rs. 55,000 Rs. 25,000 Rs. 10,000
41 . A loss of 19% gets converted into a profit on 17% when the selling price in increased
by Rs. 162. The cost price of the article is
Rs. 360 Rs. 540 Rs. 450 Rs. 600
42 . A man purchased 150 pens at the rate of Rs. 12 per pen. He said 50 pens at a gain
of 10%. The percentage gain at which he sell the remaining pens so as to gain 15%
of the whole outlay is
1
1

17% 20%
2
2

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43 . A dealer sold two types of goods for Rs. 10,000 each. On one of them, he lost 20%
and the other he gained 20%. His gain or loss percent in the entire transaction was
gain loss loss 20% gain
44 . The cost price of 40 articles is the same at the selling price of 25 articles. Find the
gain
15% 75% 65% 60%
45 . Water flows at a rate of 10 meters per minute from a cylindrical pipe 5 mm in
diameter. How long will it take to fill up a conical vessel whose diameter at the base
is 40 cm and depth is 24 cm?
48 mins 15secs
55 mins 51 mins 12 secs 52 mins 1 sec
46 . The three perpendicular distances of three sides of an equilateral triangle from a
point which lies inside that triangle are 6 cm, 9 cm and 12 cm respectively. The
perimeter of the triangle is
552cm 553cm 422 453cm
47 . The area of aright-angled triangle is 34 cm2 and one of the sides containing the
right angle is 6 cm. The altitude on the hypotenuse is
5.2 cm 12 cm 3.6 cm 4.8 cm
48 . A cost of cultivating a square field at a rate of Rs. 135 per hectare is Rs. 1,215. The
cost of putting a fence around it at the rate of 75 paise per metre would be
Rs. 900 Rs. 1,800 Rs. 360 Rs. 810
49 . The area of a trapezium is 384 cm2. IF its parallel sides are in the ratio 3 5 and the
perpendicular distance between them is 12 cm, the smaller of the parallel sides is
30 cm 36 cm 20 cm 24 cm
50 . The perimeter of the triangular base of a right prism is 60 cm and the sides of the
base are in the ratio 5 12 13. Then its volume will be (height of the prism being 50
cm)
5400 cm3 9600 cm3 6000 cm4 6600 cm3
51 . If the length of a rectangular parallelepiped is 3 times of its breadth and 5 times of
its height and its volume is 144400 cu.cm, then area of the total surface will be
4320 sq. cm 5320 sq. cm 2420 sq. cm 3320 sq. cm
52 . The capacities of two hemispherical bows are 6.4 litres and 21.6 litres respectively.
Then the ratio of their internal curved surface areas will be
2:3 16 31 4 9 2 3
53 . A man can row at 10 kmph in still water. If it takes a total of 5 hours four him to go
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to a place 24 km away and return, then the speed of the water current is

1

kmph 1 kmph 2 kmph 3 kmph
2

54 . A man started 20 minutes late and travelling at a speed of 1 1
times of his usual
2

speed reaches his office in time. The time taken by the man to reach his office at his
usual speed is

1 hour 30 minutes 40 minutes 1 hr 20 minutes
55 . Divide Rs. 15,494 A and B so that share at the end of 9 years may be equal to
share at the end of 11 years, compound interest being 20% per annum. Then
share is
Rs. 9144 Rs. 9414 Rs. 8000 Rs. 9140
56 . The principal amount which yields a compound interest or Rs. 208 in the second
year at is
Rs. 13000 Rs. 6500 Rs. 5000 Rs. 10000
57 . An amount is invested in a bank at compound rate of interest, after first and third
year is Rs. 1200 and Rs. 1587 respectively. What is the rate of interest?
12% 15% 10% 3.
58 . The difference between compound and simple rates of interest on Rs. 10000 for 3
years at p.a. is
Rs. 76.50 Rs. 76 Rs. 76.25 Rs. 76.75
59 . A solid consists of a circular cylinder with exact fitting right circular cone placed on
the top. The height of the cone is h. If total volume of the solid is three times the
volume of the cone, then the height of the circular cylinder is
3h 2h

4 h 2h
2 3

3

60 . If x
then the value of

2

x 1



is equal to

a x 1

3


3 0 1
2

61 . The area of the region bounded by y with the co-ordinate axes is
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SSC Tier-II(16-09-2012)

66 . If 28
50 sq. units 20 sq. units 25 sq. units 52 sq. units
62 . The real value of that satisfies the equation 4x-9 4x+9 5 7 is
3


4 5 23
7

63 . Find the value of a3 b3 c3 3abc when a 225, b 236, c 227.
2 034 2 340 2 304 2 430
1

64 . Number of solutions of the equation x2 2 2 x2 is
x x1



4 0 1

2

a

xa

65 . If then the value of is
3 2

x xx



2 2 a

a
a 2

(where b are rationales), value of is
2
3ab

67 .232 (22 (24 (28 (216 is equal to
216
0 1

68 . If the expression x 809436 × 809438 be a perfect square, then the value of x is
80 94 36 80 94 38 0 1
69 . If O is the orthocenter of the DABCAND ÐBAC= 80O, then measure of ÐBOCis
120o 90o 80o 100o
70 . Let A and B be two solid spheres such that the surface area of B is 300% higher than
the surface area of A. The volume of A is found to be lower than the volume of
B. The value of k must be
90 .5 87 .5 85 .5 92 .5
71 . The ratio of the areas of the circumcircle and the incircle of a square is
2 1:2 2 1 1 2
72 . From a circular sheet of paper of radius 10 cm, a sector of area 40% is removed. If
the remaining part is used to make a conical surface, then the ratio of the radius
and the height of the cone is
3 4 4 3 1 2 1 1
73 . If the area of the circular shell having inner and outer radii of 8 cm and 12 cm
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respectively is equal to the total surface area of a cylinder of radius R1 and height
then is terms of R1 will be

30 40 -R2 22

1 13R1 -30 R1 -40

R2 R 2
1 17R R

1 1

74 . A well or radius 3.5 m is dug 16 m deep. The earth removed is spread over an area
of 400 m2 to form a platform. Height of the platform is
7.7 m 77 m 1.57 m 154 m
75 . The ratio of the number of sides of two regular polygons is 1 2. If each interior
angle of the first polygon is 120o, then the measure of each interior angle of the
second polygon is
150o 160o 140o 135o
51

76 . If x

then x2 x 1 is equal to
51




5 0 1

77 . Two posts are x meters apart and the height of one is double that of the other. If
from the mid-point of the line joining their feet, an observer finds the angular
elevations of their tops to be complementary, then the height (in meters) of the
shorter post is
x 2 2
x
2
x
x
4
x
78 . If .
is a positive acute angle and tan 2 .
tan 3 .
then the value of cos2 5.
2

is

1
2

1
2
1
x
79 . If sin 17o y then the value of (sec 17o sin 73o) is
2x 2y 2y 2x
y 2 2x x 2 2x x 2 2y y 2 2y


80 . In a right-angled triangle XYZ, right-angled at if XY 26 and XZ YZ then
sec X tan X is
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SSC Tier-II(16-09-2012)


1
2

6

26


2
66

81 . If 0o .
90o, then the value of sin .
cos .
is
less than 1 equal to 2
equal to 1 greater than 1
82 . An aeroplane when flying at a height of 5000 m from the ground passes vertically
above another aeroplane at an instant, when the angles of elevation of the two
aeroplanes from the same point on the ground are 60o and 45o respectively. The
vertical distance between the aeroplanes at the instant is
.
1 ö

5000 çè

3
÷ø m
450 m
5000 31)m
5000

m
83 . The angles of a triangle are in Arithmetic Progression. The ratio of the latest angle
in degrees to the number of radians in the greatest angle is 60 p . The angles in
degrees are
40o, 50o, 90o 40o, 55o, 85o 30o, 60o, 90o 35o, 55o, 90o
84 . Suppose
DABC be a right-angled triangle where ÐA 90o, and AD BC. If DABC
40cm2 DACD 10 cm2 and AC 9 cm, then the length of BC is
4 cm 6 cm 12 cm 8 cm
85 . Two circles touch each other externally at P. AB is a direct common tangent to the
two circles, A and B are points of contact and ÐPAB 35o. Then ÐABP is
65o 75o
35o 55o
86 . The length of the common chord of two interesting circles is 24 cm. If the diameters
of the circles are 30 cm and 26 cm, then the distance between the centres in cm is
15 16
13 14
87 . In DABC D and E are points on AB and AC respectively such that DE BC and DE
divides the DABC into two parts of equal areas. Then ratio of AD and BD is
1 2 1 21
1 1 1 2 1
88 . The area of the square inscribed in a circle of radius 8 cm is
128 sq. cm 125 sq. cm 256 sq. cm 250 sq. cm
89 . X and Y are centres of circles of radii 9 cm and 2 cm respectively, XY 17 cm. Z is
the centre of a circle of radius r cm which touches the above circles externally.
Given that ÐXZY 90o, the value of r is
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9 cm 8 cm 13 cm 6 cm
90 . I is the incentre of a triangle ABC. If
ÐABC 65o and ÐACB 55o, then the value
of ÐBIC is
140o 110o 130o 120o
91 . If the radii of two circles be 6 cm and 3 cm and the length of the transverse common
tangent be 8 cm, then the distance between the two centres is
150 cm
135 cm
145 cm
140 cm
92 . The ratio between the number of sides of two regular polygons is 1 2 and the ratio
between their interior angles is 2 3. The number of sides of these polygons is
respectively
8
14
12
10
93.
The minimum value of
Sin2 .
cos2 .
sec2 .
cosec2 .
tan2 .
cot2 .
is
7 1 3
æ p xö 1
æ 1ö

94 . If 2 sin ç ÷ x2 2 then the value of ç ÷ is
è 2 ø x
è x
xø

0
2

o o

tan 57 cot 37

95 . The expression
is equal to
o o

tan 33 cot 53

tan 33o cot 53o
tan 53o cot 37o
tan 33o cot 57o
(d)tan 57o cot 37o
Directions: The bar chart g iven below s hows the p ercentag e distribu tion of the
production of various models of a mobile manufacturing company in 2007 and 2008.
The total production in 2007 was 35 lakh mobile phones and in 2008 the production
was 44 lakh. Study the chart and answer questions 96 100.

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100
90
80
70
60
50
40
30
20
10
0
2007 2008
A
B
C
D
E
F
F
A
B
C
D
E
F
A
B
C
D
E
Legend
96 . What was the difference in the number of B type mobile produced in 2007 and
20 08?
25, 000 75, 000 55, 000 70, 000
97 . If the percentage production of A type mobiles in 2008 was same as that in 2007,
then the number of A type mobile produced in 2008 would have been
11, 70, 000 10, 50, 000 14, 00, 000 13, 20, 000
98 . If 85% of the D type mobile produced in each year were sold by the company, how
many D type mobiles remained unsold?
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SSC Tier-II(16-09-2012)


1,18,500 1,22,500 76, 500 93, 500
99 . Total number of mobile of models B and E manufactured in 2007 was
21,00,000 19,25,000 24,50,000 22,75,000
10 0. For which models was the percentage variation in production from 2007 to 2008
the maximum?
D and E A and B B and C C and D
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