## SSC CHSL - Quantitative Aptitude

Quantitative Aptitude

1. This Section consists of 50 questions.

2. All questions are compulsory and carry equal marks.

3. Answer the questions quickly and as carefully as you can.

4. Some questions may be difficult and others easy.

5. Do not spend too much time on any question.

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Question 1 |

1.

**The present worth of a bill due 7 months hence is Rs. 1200 and if the bill were due at the end of 2 1/2 years its present worth would be Rs. 1016. The rate per cent is—**A | 5% |

B | 10% |

C | 15% |

D | 20% |

Question 2 |

2.

**In a quarterly examination a student secured 30% marks and failed by 12 marks. In the same examination another student secured 40% marks and got 28 marks more than minimum marks to pass. The maximum marks in the examination is—**A | 300 |

B | 500 |

C | 700 |

D | 400 |

Question 3 |

3.

**Two trains X and Y start from Jodhpur to Jaipur and from Jaipur to Jodhpur respectively. After passing each other they take 4 hr 48 minutes and 3 hr 20 minutes to reach Jaipur and Jodhpur respectively. If X is moving at 45 km/hr, the speed of Y is—**A | 60 km/hr |

B | 58 km/hr |

C | 54 km/hr |

D | 64·8 km/hr |

Question 4 |

4.

**A sum doubles itself in 16 years, then in how many years will it treble itself; rate of interest being simple—**A | 25 years |

B | 24 years |

C | 48 years |

D | 64 years |

Question 5 |

5.

**A right circular cylinder is circumscribed about a hemisphere so that they share the same base. The ratio of the volumes of cylinder and hemisphere is—**A | 4 : 3 |

B | 3 : 1 |

C | 3 : 4 |

D | 3 : 2 |

Question 6 |

6.

**The ratio of volumes of two cubes is 8 : 125. The ratio of their surface areas is—**A | 4 : 25 |

B | 2 : 75 |

C | 2 : 15 |

D | 4 : 15 |

Question 7 |

7.

**If the sides of an equilateral triangle be increased by 1 m its area is increased by √ 3 sq m. The length of any of its sides is—**A | 2 m |

B | 5/2 m |

C | 3/2 m |

D | √ 3 m |

Question 8 |

8.

**A TV was bought at a price of Rs. 21,000. After one year the value of TV was depreciated by 5%. Find the value of the TV after one year—**A | Rs.19,950 |

B | Rs. 20,950 |

C | Rs. 18,950 |

D | Rs. 17,950 |

Question 9 |

9.

**The listed price of a shirt is Rs. 270 and it is available at Rs. 237.60. The rate of discount is—**A | 10% |

B | 12% |

C | 15% |

D | 20% |

Question 10 |

10.

**The ratio of 3 positive numbers is 2 : 3 : 5 and the sum of their squares is 608. The three numbers are—**A | 2, 3, 5 |

B | 10, 15, 25 |

C | 8, 12, 20 |

D | 4, 6, 10 |

Question 11 |

11.

**A sum of money is divided among A, B, C and D in the proportion of 7 : 6 : 3 : 5. If B gets Rs. 270 more than C, then share of D is—**A | Rs. 250 |

B | Rs. 350 |

C | Rs. 450 |

D | Rs. 455 |

Question 12 |

12.

**A motorist travels to a place 150 km away at an average speed of 50 km/hr and returns at 30 km/hr. His average speed for the whole journey in km/hr is—**A | 37·5 |

B | 37 |

C | 35 |

D | 40 |

Question 13 |

13.

**Three numbers are such that the average of first two numbers is 2, the average of the last two numbers is 3 and the average of the first and the last numbers is 4, then the average of three numbers is equal to—**A | 2 |

B | 3.5 |

C | 3 |

D | 2.5 |

Question 14 |

14.

**A manufacturer sells an item to a wholesale dealer at a profit of 18%. The wholesaler sells the same to a retailer at a profit of 20%. The retailer in turn sells it to a customer for Rs. 15045 thereby earning a profit of 25%. The cost price of the manufacturer is—**A | Rs. 8000 |

B | Rs. 8500 |

C | Rs. 9000 |

D | Rs. 10000 |

Question 15 |

15.

**A shopkeeper buys two cameras at the same price. He sells one camera at a profit of 18% and the other at a price 10% less than the selling price of the first. His total profit or loss per cent is—**A | 12·1% profit |

B | 12·1% loss |

C | 12·2% profit |

D | 11·1% loss |

Question 16 |

16.

A | (2 +√ 3) : (2 –√ 3) |

B | (2 – √ 3) : (2 +√ 3) |

C | (3 +√ 2) : (3 –√ 2) |

D | (3 – √ 2) : (3 +√ 2) |

Question 17 |

17.

**If the sides of a triangle is extended in both the sides then the sum of the exterior angles so formed in both sides is—**A | 360° |

B | 540° |

C | 720° |

D | 180° |

Question 18 |

18.

A | 4/5 |

B | 5/4 |

C | 3/4 |

D | 3/5 |

Question 19 |

19.

A | 3 cm |

B | 24 cm |

C | 16 cm |

D | 48 cm |

Question 20 |

20.

**In Δ ABC the straight line parallel to the side BC meets AB and AC at the points P and Q respectively. If AP = QC the length of AB is 12 units and the length of AQ is 2 units then the length (in units) of CQ is—**A | 4 |

B | 6 |

C | 8 |

D | 10 |

Question 21 |

21.

**In a circle if PQ is the diameter of the circle and R is on the circumference of the circle such that ∠PQR = 30°, then ∠RPQ =**A | 90° |

B | 60° |

C | 30° |

D | 45° |

Question 22 |

22.

A | –1 |

B | 1 |

C | 2 |

D | 3 |

Question 23 |

23.

**If sec θ + tan θ = 2 +√3, then the value of sec θ is—**A | √3 |

B | 2 |

C | 4 |

D | 2√3 |

Question 24 |

24.

**A hemisphere of iron is melted and recast in the shape of a right circular cylinder of diameter 18 cm and height 162 cm. The radius of the hemisphere is—**A | 27 cm |

B | 9 cm |

C | 6 cm |

D | 12 cm |

Question 25 |

25.

**An iron sphere of radius 27 cm is melted to form a wire of length 729 cm. The radius of wire is—**A | 6 cm |

B | 9 cm |

C | 18 cm |

D | 36 cm |

Question 26 |

26.

**The base of a triangle is increased by 10%. To keep the area unchanged the height of the triangle is to be decreased by—**A | 9 1/11% |

B | 11 1/9% |

C | 11% |

D | 9% |

Question 27 |

27.

**If m + n = – 2, then the value of m^3 + n^3 – 6mn is—**A | 8 |

B | 4 |

C | -8 |

D | -4 |

Question 28 |

28.

A | 1/2 |

B | 1/3 |

C | 2/5 |

D | 5/6 |

Question 29 |

29.

A | 4 |

B | 3 |

C | 2 |

D | 5 |

Question 30 |

30.

**If x = 5, y = 6 and z = – 11, then the value of x^3 + y^3 + z^3 is—**A | –890 |

B | –970 |

C | –870 |

D | –990 |

Question 31 |

31.

**If 9 √ x = √ 12 + √ 147, then x =**A | 5 |

B | 3 |

C | 2 |

D | 4 |

Question 32 |

32.

**There are 24 peaches, 36 apricots and 60 bananas and they have to be arranged in several rows in such a way that every row contains the same number of fruits of only one type. What is the minimum number of rows required for this to happen ?**A | 12 |

B | 9 |

C | 10 |

D | 6 |

Question 33 |

33.

**If n is even (6^n – 1) is divisible by—**A | 37 |

B | 35 |

C | 30 |

D | 6 |

Question 34 |

34.

**I have x marbles. My elder brother has 3 more than mine, while my younger brother has 3 less than mine. If the total number of marbles is 15, the number of marbles that I have is—**A | 3 |

B | 5 |

C | 8 |

D | 7 |

Question 35 |

35.

**Weight of a bucket when filled fully with water is 17 kg. If the weight of the bucket when half filled with water is 13·5 kg what is the weight of empty bucket ?**A | 12 kg |

B | 8 kg |

C | 10 kg |

D | 7 kg |

Question 35 Explanation:

The weight of empty bucket
= 13·5 × 2 – 17
= 27 – 17
= 10 kg

Question 36 |

36.

**Some staff promised to do a job in 18 days, but 6 of them went on leave. So the remaining men took 20 days to complete the job. How many men were there originally ?**A | 55 |

B | 62 |

C | 56 |

D | 60 |

Question 36 Explanation:

Let there were x men originally.
Then,
x × 18 = (x – 6) × 20
2x = 6 × 20
x = 60

Question 37 |

37.

**A certain number of men can do a piece of work in 40 days. If there were 45 men more the work could have been finished in 25 days. Find the original number of men employed in the work—**A | 70 |

B | 85 |

C | 65 |

D | 75 |

Question 37 Explanation:

Let the original number of
men employed in the work = x
Then, x × 40 = (x + 45) × 25
15x = 45 × 25
x = 75

Question 38 |

38.

**A brick 2′′ thick is placed against a wheel to act for a stop. The horizontal distance of the face of the brick from the point where the wheel touches the ground is 6′′. The radius of the wheel in inches is—**A | 10 |

B | 5 |

C | 12 |

D | 6 |

Question 39 |

39.

**If sin (60° – x) = cos (y + 60°), then the value of sin (x – y) is—**A | 1/ √2 |

B | 1/2 |

C | √3/2 |

D | 1 |

Question 40 |

40.

A | – 1 |

B | 0 |

C | 1 |

D | 2 |

Question 41 |

41.

**If 0° < θ < 90° and 2 sin^2 θ + 3 cos θ = 3, then the value of θ is—**A | 30° |

B | 60° |

C | 45° |

D | 75° |

Question 42 |

**Directions—(Q. 42 to 45) The following graph represents the transport used by children. Study the graph and answer.**

42. What is the measure of the angle at the centre representing people walking ?

A | 144° |

B | 48° |

C | 36° |

D | 72° |

Question 42 Explanation:

Required angle
= 360° – (120° + 72° + 24°)
= 360° – 216°
= 144°

Question 43 |

**Directions—(Q. 42 to 45) The following graph represents the transport used by children. Study the graph and answer.**

43. What is the percentage of children using scooter ?

A | 20% |

B | 33 1/3% |

C | 15% |

D | 40% |

Question 44 |

**Directions—(Q. 42 to 45) The following graph represents the transport used by children. Study the graph and answer.**

44. If 10 students come by car, how many come by bus ?

A | 60 |

B | 50 |

C | 30 |

D | 100 |

Question 45 |

45. If 180 students come walking to school what is the strength of the school ?

A | 540 |

B | 450 |

C | 360 |

D | 600 |

Question 46 |

**Directions—(Q. 46 to 50) Sales of Books (in thousand numbers) from Six Branches—B1, B2, B3, B4, B5 and B6 of a publishing company in 2009 and 2010. Study the graph and answer.**

46. The ratio of the total sales of branch B2 for both years to the total sales of branch B4 for both years is—

A | 7 : 9 |

B | 2 : 3 |

C | 4 : 5 |

D | 3 : 5 |

Question 47 |

**Directions—(Q. 46 to 50) Sales of Books (in thousand numbers) from Six Branches—B1, B2, B3, B4, B5 and B6 of a publishing company in 2009 and 2010. Study the graph and answer.**

47. Total sales of branch B6 for both the years is x per cent of the total sales of branches B3 for both the years. The value of x is—

A | 68·54% |

B | 73·17% |

C | 71·11% |

D | 75·55% |

Question 48 |

**Directions—(Q. 46 to 50) Sales of Books (in thousand numbers) from Six Branches—B1, B2, B3, B4, B5 and B6 of a publishing company in 2009 and 2010. Study the graph and answer.**

48. x% of the average sales of branches B1, B2 and B3 in 2010 is the average sales of branches B1, B3 and B6 in 2009. The value of x is—

A | 77·5% |

B | 87·5% |

C | 82·5% |

D | 75% |

Question 49 |

49. The average sales of all the branches for the year 2009 is—

A | 73 |

B | 83 |

C | 80 |

D | 88 |

Question 50 |

50. Total sales of branches B1, B3 and B5 together for both the years is—

A | 250 |

B | 310 |

C | 435 |

D | 560 |

Question 50 Explanation:

(D) Total sales of branches B1,
B3 and B5
= (80 + 105) + (95 + 110)
+ (75 + 95)
= 185 + 205 + 170
= 560

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