## 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.

A | a = 729 |

B | a < 729 but a > 216 |

C | a < 216 |

D | a > 729 |

Question 2 |

2.

**The number of prime factors in 6^333 × 7^222 × 8^111 is—**A | 1211 |

B | 1221 |

C | 1222 |

D | 1111 |

Question 3 |

3.

**In a particular type of alloy the ratio of lead to tin is 5 : 6. The amount of lead should be added to 12·1 kg of this material to make the ratio 1 : 1 is—**A | 1·1 kg |

B | 1 kg |

C | 0·9 kg |

D | 1·5 kg |

Question 4 |

4.

A | 2 |

B | 1 |

C | 4 |

D | 3 |

Question 5 |

5.

**If 120 is 20% of a number, then 120% of that number will be—**A | 120 |

B | 360 |

C | 720 |

D | 20 |

Question 6 |

6.

**In a division sum, the divisor is 3 times the quotient and 6 times the remainder. If the remainder is 2, then the dividend is—**A | 28 |

B | 50 |

C | 48 |

D | 36 |

Question 6 Explanation:

Divisor = 3 × Quotient
= 6 × Remainder
= 6 × 2
Divisor = 12
Quotient = 4
Dividend = Divisor × Quotient
+ Remainder
= 12 × 4 + 2
= 48 + 2 = 50

Question 7 |

7.

A | 99900 |

B | 1 |

C | 99000 |

D | 99800 |

Question 8 |

8.

A | 55/28 |

B | 55/42 |

C | 45/56 |

D | 45/28 |

Question 9 |

9.

**Zinc and copper are in the ratio 5 : 3 in 400 gm of an alloy. How much of copper (in grams) should be added to make the ratio 5 : 4 ?**A | 200 |

B | 50 |

C | 66 |

D | 72 |

Question 10 |

10.

**The average age of A and B is 20 years. If A is to be replaced by C, the average would be 19 years. The average age of C and A is 21 years. The ages of A, B and C in order (in years) are—**A | 22, 20, 18 |

B | 18, 22, 20 |

C | 18, 20, 22 |

D | 22, 18, 20 |

Question 10 Explanation:

Let the ages of A, B and C
are x, y and z respectively.
Then average age of A and B =
20
x + y = 40
y + z = 19 × 2
= 38
z + x = 21 × 2
= 42
Now, 2 (x + y + z) = 120
x + y + z = 60
On solving we get—
x = 22 years,
y = 18 years
z = 20 years

Question 11 |

11.

**A reduction of 10% in the price of a commodity enables a person to buy 25 kg more for Rs. 225. The original price of the commodity per kg was—**A | Rs. 1·50 |

B | Rs. 2 |

C | Rs. 1 |

D | Rs. 2.50 |

Question 12 |

12.

**One type of liquid contains 20% water and the second type of liquid contains 35% of water. A glass is filled with 10 parts of first liquid and 4 parts of second liquid. The water in the new mixture in the glass is—**A | 24 2/7% |

B | 37% |

C | 46% |

D | 12 1/7% |

Question 13 |

13.

A | 37/48 |

B | 13/27 |

C | 1/2 |

D | 73/84 |

Question 14 |

14.

**Mohan sold his watch at 10% loss. If he had sold it for Rs. 45 more, he would have made 5% profit. The selling price (in Rs) of the watch was—**A | 270 |

B | 300 |

C | 900 |

D | 110 |

Question 15 |

15.

**A vendor loses the selling price of 4 oranges on selling 36 oranges. His loss per cent is—**A | 11 1/2% |

B | 12 1/2% |

C | 9% |

D | 10% |

Question 16 |

16.

**Successive discounts of 30% and 20% is equivalent to a single discount of—**A | 10% |

B | 50% |

C | 40% |

D | 44% |

Question 17 |

17.

**At the beginning of a partnership business, the capital of B was 3/2 times that of A. After 8 months B withdrew 1/2 of his capital and after 10 months A withdrew 1/4 th of his capital. At the end of the year, if the profit incurred is Rs. 53,000, find the amount received by A.**A | Rs. 23,000 |

B | Rs. 30,800 |

C | Rs. 32,000 |

D | Rs. 30,000 |

Question 18 |

18.

**If x, y, z are three sums of money such that y is the simple interest on x and z is the simple interest on y for the same time and at the same rate of interest, then we have—**A | y^2 = zx |

B | z^2 = xy |

C | xyz = 1 |

D | x^2 = yz |

Question 19 |

19.

**A and B can together finish a work in 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. The number of days in which B alone can finish the work is—**A | 60 |

B | 50 |

C | 48 |

D | 54 |

Question 20 |

20.

**Options :**A | D is the correct answer |

Question 21 |

21.

**If 6x – 5y = 13, 7x + 2y = 23, then 11x + 18y =—**A | 15 |

B | -15 |

C | 51 |

D | 33 |

Question 21 Explanation:

6x – 5y = 13
7x + 2y = 23
On solving, x = 3,
y = 1
Now,
11x + 18y = 11 × 3 + 18 × 1
= 33 + 18
= 51

Question 22 |

22.

**If x + y + z = 13 and x^2 + y^2 + z^2 = 69, then the value of xy + z (x + y) is equal to—**A | 60 |

B | 70 |

C | 40 |

D | 50 |

Question 22 Explanation:

x + y + z = 13
Taking square both side—
x2 + y2 + z2 + 2 (xy + yz + zx)
= 169
69 + 2 (xy + yz + zx) = 169
2 (xy + yz + zx) = 100
xy + yz + zx = 50
xy + z (x + y) = 50

Question 23 |

23.

**Two trains, of same length, are running in parallel tracks in the same direction with speed 60 km/ hour and 90 km/hour respectively. The latter completely crosses the former in 30 seconds. The length of each train (in metres) is—**A | 115 |

B | 125 |

C | 150 |

D | 100 |

Question 24 |

24.

**ABC is an isosceles triangle with AB = AC. The side BA is produced to D such that AB = AD. If ∠ ABC = 30°, then ∠ BCD is equal to—**A | 60° |

B | 45° |

C | 90° |

D | 30° |

Question 25 |

25.

**ABCD is a trapezium in which AB || DC and AB = 2 CD. The diagonals AC and BD meet at O. The ratio of areas of triangles AOB and COD is—**A | 1 : 4 |

B | 1 : 2 |

C | 1 : √2 |

D | 4 : 1 |

Question 26 |

26.

**PQ is a chord of length 8 cm, of a circle with centre O and of radius 5 cm. The tangents at P and Q intersect at a point T. The length of TP is—**A | 15/4 cm |

B | 20/3 cm |

C | 21/4 cm |

D | 10/3 cm |

Question 27 |

27.

**The area of the triangle formed by the graphs of 3x + 4y = 12, xaxis and y-axis (in sq. units) is—**A | 8 |

B | 4 |

C | 12 |

D | 6 |

Question 28 |

28.

A | 4 |

B | 8 |

C | 9 |

D | 2 |

Question 29 |

29.

**The side QR of an equilateral triangle PQR is produced to the point S in such a way that QR = RS and P is joined to S. Then the measure of ∠ PSR is—**A | 45° |

B | 30° |

C | 15° |

D | 60° |

Question 30 |

30.

**Three solid iron cubes of edges 4 cm, 5 cm and 6 cm are melted together to make a new cube. 62 cm3 of the melted material is lost due to improper handling. The area (in cm2) of the whole surface of the newly formed cube is—**A | 216 |

B | 294 |

C | 343 |

D | 125 |

Question 31 |

31.

**If the ratio of volumes of two cones is 2 : 3 and the ratio of the radii of their bases is 1 : 2, then the ratio of their heights will be—**A | 8 : 3 |

B | 3 : 4 |

C | 4 : 3 |

D | 3 : 8 |

Question 32 |

32.

**A right pyramid stands on a base 16 cm square and its height is 15 cm. The area (in cm^2) of its slant surface is—**A | 444 |

B | 514 |

C | 544 |

D | 344 |

Question 33 |

33.

**If a chord of a circle is equal to the radius of the circle, then the angle subtended by the chord at a point on the minor arc is—**A | 30° |

B | 150° |

C | 60° |

D | 120° |

Question 34 |

34.

**The length of each side of a rhombus is equal to the length of the side of a square whose diagonal is 40 √2 cm. If the lengths of the diagonals of the rhombus are in the ratio 3 : 4, then its area (in cm^2) is—**A | 1536 |

B | 1550 |

C | 1600 |

D | 1535 |

Question 35 |

35.

**The altitude drawn to the base of an isosceles triangle is 8 cm and its perimeter is 64 cm. The area (in cm^2) of the triangle is—**A | 120 |

B | 240 |

C | 180 |

D | 360 |

Question 36 |

36.

**The product cos 1° cos 2° cos 3° cos 4° … cos 100° is equal to—**A | 0 |

B | -1 |

C | 1/4 |

D | 1 |

Question 36 Explanation:

cos 1° cos 2° cos 3° cos 4°
… cos 100°
= cos 1° cos 2° cos 3° … cos 90°
… cos 100°
= cos 1° cos 2° cos 3° … × 0 × …
cos 100° (Q cos 90° = 0)
= 0

Question 37 |

37.

**The greatest value of sin^4 θ + cos^4 θ is—**A | 1 |

B | 2 |

C | 3 |

D | 1/2 |

Question 38 |

38.

**If 3 sin θ + 5 cos θ = 5, then 5 sin θ – 3 cos θ is equal to—**A | ± 2 |

B | ± 3 |

C | ± 5 |

D | 1 |

Question 39 |

39.

**If sin θ + sin^2 θ = 1, then the value of cos^2 θ + cos^4 θ is—**A | 1 |

B | 2 |

C | 4 |

D | 0 |

Question 40 |

40.

**From two points on the ground and lying on a straight line through the foot of a pillar, the two angles of elevation of the top of the pillar are complementary to each other. If the distances of the two points from the foot of the pillar are 9 metres and 16 metres and the two points lie on the same side of the pillar, then the height of the pillar is—**A | 12 m |

B | 5 m |

C | 10 m |

D | 7 m |

Question 41 |

41.

**The sum of interior angles of a regular polygon is 1440°. The number of sides of the polygon is—**A | 8 |

B | 10 |

C | 12 |

D | 6 |

Question 42 |

42.

**The base of a right prism is a right-angled triangle whose sides are 5 cm, 12 cm, 13 cm. If the area of the total surface of the prism is 360 cm^2, then its height (in cm) is—**A | 11 |

B | 10 |

C | 12 |

D | 9 |

Question 43 |

43.

**LCM of two numbers is 2079 and their HCF is 27. If one of the numbers is 189, the other number is—**A | 216 |

B | 297 |

C | 584 |

D | 189 |

Question 44 |

44.

**Three pipes A, B and C can fill a tank in 6 hours. After working together for 2 hours, C is closed and A and B fill the tank in 8 hours. The time (in hours) in which the tank can be filled by pipe C alone is—**A | 9 |

B | 10 |

C | 12 |

D | 8 |

Question 45 |

45.

**The radii of two circles are 10 cm and 24 cm. The radius of a circle whose area is the sum of the areas of these two circles is—**A | 26 cm |

B | 36 cm |

C | 17 cm |

D | 34 cm |

Question 46 |

46.

A | 0 |

B | 1 |

C | 2 |

D | -1 |

Question 47 |

47.

47. If the difference between the number of people in the age groups 46–55 and 16–25 is 0·975 million, then the total population (in millions) of the city is—

**Directions—(Q. 47 and 48) In these questions the table shows the percentage of total population of a city in different age groups. Study the table and answer questions.**47. If the difference between the number of people in the age groups 46–55 and 16–25 is 0·975 million, then the total population (in millions) of the city is—

A | 25 |

B | 27 |

C | 30 |

D | 22 |

Question 48 |

**Directions—(Q. 47 and 48) In these questions the table shows the percentage of total population of a city in different age groups. Study the table and answer questions.**

48. If there are 22 million people below 36 years, then the number of people (in millions) in the age group 56 – 65 is—

A | 3.5 |

B | 5 |

C | 5.5 |

D | 3 |

Question 49 |

49.

49. In 2005, the exports of company X were double that of company Y in that year. If the imports of company X during the year were Rs. 180 crore, what was the amount (in crore Rs) of imports of company Y during the year ?

**Directions—(Q. 49 and 50) Study the following graph and answer questions.**49. In 2005, the exports of company X were double that of company Y in that year. If the imports of company X during the year were Rs. 180 crore, what was the amount (in crore Rs) of imports of company Y during the year ?

A | 282 |

B | 212 |

C | 210 |

D | 315 |

Question 50 |

**Directions—(Q. 49 and 50) Study the following graph and answer questions.**

50. If the imports of company X in 2007 were increased by 40%, what would be the ratio of exports to the increased imports ?

A | 0·75 |

B | 1·25 |

C | 1·75 |

D | 0·25 |

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