# SSC CGL Quantitative Aptitude Questions For Practice [Tier 2] | Solve Here

Everything has come on halt due to the lockdown, many exams have been postponed for now and will happen after a certain period. But there should be no halt in your exam preparations during this lockdown. To help you with your exam preparation we are starting a series on SSC CGL Quantitative Aptitude Questions for Tier 2 that will help you for the upcoming Tier of SSC CGL examination.

SSC CGL Quantitative Aptitude is arguably one of the toughest sections of the SSC CGL Exam. All the topics in this section require extra effort and practice. Mastering the topics in the SSC CGL Tier 2 Quantitative Aptitude section is the key to achieve an above-average score in the

Keeping in mind the toughness level of the SSC CGL Quant Section we have brought you the topic-wise SSC CGL Quantitative Aptitude Questions for Tier 2. Read along to know the important questions and practice them to score the highest in the SSC CGL Quantitative Section.

## 1. SSC CGL Quantitative Aptitude Questions For Tier 2:

### 1.1 SSC CGL Quantitative Aptitude Questions For Practice For Tier 2: Set 3

Q1) Unit digit in (264)102 + (264)103 is:

(a) 0
(b) 4
(c) 6
(d) 8

Q2) In a class 3/5 of the students are girls and the rest are boys. If 2/9 of the girls and 1/4 of the boys are absent. What part of the total number of students are present?

(a) 23/30
(b) 23/36
(c) 18/49
(d) 17/25

Q3) The maximum number of students among whom 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and the same number of pencils is:

(a) 91
(b) 910
(c) 1001
(d) 1911

Q4) The following points (3a, 0), (0, 3b), (a, 2b) forms a

(a) straight line
(b) triangle
(c) equilateral triangle
(d) None of these

Q5) The points A(–1, 4), B(5, 2) are the vertices of a triangle of which C(0,–3) is the centroid, then the third vertex C is

(a) 4, 15
(b) 4, –15
(c) –4, –15
(d) None of these

Q6) The Acute angle between the lines with slopes 3/4 and –1/7 is

(a) 60°
(b) 45°
(c) 30°
(d) None of these

Q7) Between two consecutive years my incomes are in the ratio of 2 : 3 and expenses in the ratio 5: 9. If my income in the second year is Rs. 45000 and my expenses in the first year is Rs. 25000 my total savings for the two years are

(a) Nil
(b) Rs. 15000
(c) Rs. 10000
(d) Rs. 5000

Q8) Rs. 180 contained in a box consists of one rupee, 50 paise, and 25 paise coins in the ratio 2 : 3: 4. What is the number of 50 paise coins?

(a) 60
(b) 120
(c) 150
(d) 180

Q9) On simplification of We get:

(a) 1
(b) 4
(c) 5
(d) 6

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Q10) Evaluate  Q11) Assume that (a) 36,164
(b) 37,304
(c) 36,304
(d) 37,164

Q12) A boy rides his bicycle 10km at an average speed of 12 km per hr and again travels 12 km at an average speed of 10 km per hr His average speed for the entire trip is approximate:

(a) 10.4km/hr
(b) 11.0 km/hr
(c) 12.2 km/hr
(d) 10.8 km/hr

Q13) If a man walks 20 km at 5 km/hr, he will be late by 40 minutes. If he walks at 8 km per hr, how early from the fixed time will he reach?

(a) 50 minutes
(b) 15 minutes
(c) 25 minutes
(d) ¹(½) hours

Q14) The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/ hr Another train starts from B at 9 a.m. and travels towards A at 75 km/hr At what time do they meet?

(a) 11 a.m.
(b) 11: 30 a.m.
(c) 10 a.m.
(d) 10: 30 a.m.

Q15)The incomes of A, B, and C are in the ratio 3: 7: 4 and their expenses in the ratio 4 : 3: 5. If A saves Rs. 300 out of an income of Rs. 2,400, the savings of B and C are

(a) Rs. 4.025 and Rs. 575
(b) Rs. 1.575 and Rs 2.625
(c) Rs. 2.750 and Rs. 1.525
(d) Rs. 3.725 and Rs. 1.525

### 1.2 SSC CGL Quant Practice Questions For Tier 2 Examination: Set 2

Q1) N solid metallic spherical balls are melted and recast into a cylindrical rod whose radius is 3  times that of a spherical ball and height is 4 times the radius of a spherical ball. The value of N  is:

(1) 30
(2) 27
(3) 24
(4) 36

2. What is the area (in square units) of the triangular region enclosed by the graphs of the equations x + y = 3, 2x + 5y = 12, and the x-axis?

(1) 2
(2) 3
(3) 4
(4) 6

3. If sec Θ + tan Θ = p, (p>1) then (cosec Θ + 1) / (cosec Θ -1) = ?

(1) (p+1) / (p-1)
(2) p²
(3) (p-1) / (p+1)
(4) 2p²

4.  The value cosec (67º + θ) – sec (23º – θ) + cos15° cos35º cosec55º cos60º cosec75° is:

(1) 2
(2) 0
(3) 1
(4) 1/2

5. 35% of goods were sold at a profit of 65%, while the remaining were sold at x% loss. If the overall loss is 12%, then what is the value of x? (correct to one decimal place)

(1) 51.8
(2) 50.6
(3) 53.5
(4) 52.4

6. In a circle with centre O, ABCD is a cyclic quadrilateral and AC is the diameter. Chords AB and CD  are produced to meet at E. If ∠CAE = 34° and ∠E = 30°, then ∠CBD is equal to:

(1) 36°
(2) 26°
(3) 24°
(4) 34°

7. ab (a – b) + bc (b – c) + ca (c – a) is equal to:

(1) (a + b) (b – c) (c – a)
(2) (a – b) (b + c) (c – a)
(3) (a – b) (b – c) (c – a)
(4) (b – a) (b – c) (c – a)

8. The radius of the base of a right circular cylinder is increased by 20%. By what percent should its height be reduced so that its volume remains the same as before?

(1) 25
(2) 30 2/9
(3) 30 5/9
(4) 28

9.  A is as efficient as B and C together. Working together A and B can complete a work in 36 days and C alone can complete it in 60 days. A and C work together for 10 days. B alone will complete  the remaining work in:

(1) 110 days
(2) 88 days
(3) 84 days
(4) 90 days

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10. If 2cos2θ + 3sinθ = 3, where 0° < θ < 90°, then what is the value of sin22θ + cos2θ + tan22θ + cosec22θ?

(1) 35/12
(2) 29/3
(3) 35/6
(4) 29/6

11. The radius and the height of a right circular cone are in the ratio 5:12. Its curved surface area  is 816.4 cm2. What is the volume (in cm3) of the cone? (Take π = 3.14)

(1) 2512
(2) 1256
(3) 3140
(4) 628

12.  Given that (5x – 3)³ + (2x + 5)³ + 27 (4 – 3x)³= 9 (3 – 5x) (2x + 5) (3x – 4), then the value  of (2x + 1) is:

(1) -13
(2) 15
(3) -15
(4) 13

13.  The sides of a triangle are 12 cm, 35 cm, and 37 cm. What is the circumradius of the triangle?

(1) 19 cm
(2) 17.5 cm
(3) 17 cm
(4) 18.5 cm

14. A vessel contains a 32-liter solution of acid and water in which the ratio of acid and water is  5:3. If 12 liters of the solution is taken out and 7 1/2 liters of water are added to it, then what is the ratio of acid and water in the resulting solution?

(1) 4:7
(2) 5:6
(3) 4:9
(4) 8:11

15. A sphere of the maximum volume is cut out from a solid hemisphere. What is the ratio of the volume of the sphere to that of the remaining solid?

(1) 1:4
(2) 1:2
(3) 1:3
(4) 1:1

### 1.3 SSC CGL Quantitative Aptitude Questions For Tier 2: Set 1

1. The value of (7 + 8 x 8 ÷ 8 of 8 + 8 ÷ 8 x 4 of 4) / (4 ÷ 4 of 4 + 4 x 4 ÷ 4 – 4 ÷ 4 of 2) is:

(1) 7.8
(2) 4.6
(3) 8.7
(4) 6.4

2. To do a certain work, the ratio of efficiency of A to that of B is 3:7. Working together, they can complete the work in 10 ½ days. They work together for 8 days. 60% of the remaining work will be  completed by A alone in:

(1) 5 ½ days
(2) 5 days
(3) 6 ½ days
(4) 4 days

3. The average of thirteen numbers is 47. The average of the first three numbers is 39 and that of the next seven numbers is 49. The 11th number is two times the 12th number and the 12th number is 3 less than the 13th number. What is the average of 11th and 13th numbers?

(1) 54.5
(2) 57
(3) 56
(4) 55.5

4.  The graphs of the equations 3x + y – 5 = 0 and 2x – y – 5 = 0 intersect at the point P (α, β). What is the value of (3α + β)?

(1) 4
(2) -4
(3) 3
(4) 5

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5.  The sides AB and AC of Δ ABC are produced to P and Q respectively. The bisectors of ∠CBP and ∠BCQ meet at R. If the measure of ∠A is 44º, then what is the measure of (1/2) ∠BRC?

(1) 33°
(2) 38°
(3) 34°
(4) 32º

6. In Δ ABC, D is a point on side BC such that ∠ADC = ∠BAC. If CA = 12cm, CB = 8 cm, then CD is equal to:

(1) 12cm
(2) 15cm
(3) 18cm
(4) 16cm

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7.  A person marks his goods x% above the cost price and allows a discount of 30% on the marked price. If his profit is 5%, then the value of x will be:

(1) 50
(2) 60
(3) 45
(4) 35

8.  A right circular cylinder of the maximum volume is cut out from a solid wooden cube. The material left is what percent of the volume (nearest to an integer) of the original cube?

(1) 19
(2) 28
(3) 23
(4) 21

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9. The ratio of the volumes of two-cylinder is x:y and the ratio of their diameters is a:b. What is the ratio of their heights?

(1) xb:ya
(2) xa:yb
(3) xb²:ya²
(4) xa²:yb²

10. If A is 28% more than B and C is 25% less than the sum of A and B, then by what percent will C be more than A (correct to one decimal place)?

(1) 32.2%
(2) 28%
(3) 43%
(4) 33.6%

11. A shopkeeper bought 120 quintals of wheat. 20% of it was sold at a 25% loss. At what percent gain should he sell the rest to gain 25% on the whole transaction?

(1) 36 1/2
(2) 40
(3) 37 1/2
(4) 35

12. Anu sold an article for Rs. 480 at some profit. Had she sold it for Rs. 400, then there would have been a loss equal to one-third of the initial profit. What was the cost price of the article?

(1) Rs. 450
(2) Rs. 430
(3) Rs. 425
(4) Rs. 420

13. Pipes A, B, and C can fill a tank in 30h, 40h, and 60h respectively. Pipes A, B, and C are opened at 7  a.m., 8 a.m. and 10 a.m., respectively on the same day. When will the tank be full?

(1) 10.00 p.m.
(2) 10.20 p.m.
(3) 9.20 p.m.
(4) 9.40 p.m.

14. If the radius of a right circular cylinder is decreased by 20% while its height is increased by  40%, then the percentage change in its volume will be:

(1) 1.04% increase
(2) 10.4% decrease
(3) No increase or decrease
(4) 10.4% increase

15. The number of students in a class is 75, out of which 33 1/3% are boys and the rest are girls. The average score in mathematics of the boys is 66 2/3% more than that of the girls. If the average  score of all students is 66, then the average score of the girls is:

(1) 52
(2) 55
(3) 54
(4) 58

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## 2. Want to Practice More SSC CGL Quant Questions For Tier 1? Solve Here

### 2.1 SSC CGL Quantitative Aptitude Questions For Practice (Tier 1)

Find below the SSC CGL Quantitative Aptitude Questions topic-wise important for SSC CGL Tier 1 examination

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SSC CGL Quantitative Aptitude Questions – Important Speed, Time & Distance Questions

Q1. A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?

(a) 50 meters

(b) 100 meters

(c) 120 meters

(d) None of the above

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Q2. A man in a train notices that he can count 41 telephone posts in one minute. If they are known to be 50 metres apart, then at what speed is the train traveling?

(a) 100 Km/hr

(b) 110 Km/Hr

(c) 120 Km/Hr

(d) 150 Km/Hr

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Q3. A cyclist covers a distance of 750 meters in 2 minutes 30 seconds. What is the speed in km/hr of the cyclist?

(a) 18 Km/hr

(b) 20 Km/Hr

(c) 15 Km/Hr

(d) 7.5 Km/Hr

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Q4. Excluding stoppages, the speed of a bus is 54 km/h and including stoppages, it is 45 km/h. For how many minutes does the bus stop per hour?

(a) 5 mins

(b) 10 mins

(c) 15 mins

(d) 7.5 12 mins

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SSC CGL Quantitative Aptitude Questions – Important Geometry Questions

Q1) In a Δ ABC, if D and E are the points on the sides AB and AC respectively such that DE || BC and if AD = x , DB = x – 2 , AE = x + 2 and EC = x – 1. then find the value of x.

A. 5
B. 4
C. 3
D. 2

Explanation:

B

Since DE || BC ⇒ x/x-2 = x+2/x-1
⇒ x2 – x = x2 – 4
⇒ x(x –1) = (x +2)(x –2)

⇒ x = 4

Hence, option B is correct.

Q2) In ΔABC, AB = AC, ∠B = 70°, ∠BAD = 80°, ∠ADE = ? A. 150°
B. 135°
C. 140°
D. 120°

Explanation:

A ∠B = ∠ACB = 70°
∠BAC = 180° – (70° + 70°) = 40°

Hence, option A is correct.

SSC CGL Quantitative Aptitude Questions – Important Data Interpretation Questions

Ques.1-5. Study the following graph carefully and answer the related questions. Line graph shows the stream speed and effective speeds in the direction of boat A and in the opposite direction of boat B during 6 days of a week. 1. The difference between effective speeds of boat B on Monday and Tuesday when the stream is flowing in the direction of boat B is what percent more or less than the effective speed of the same boat on Saturday when the stream is flowing opposite to it?
a) 50%
b) 75%
c) 100%
d) 120%
e) 150%
2. If boat A traveled for 30 km and 20 km upstream on Tuesday and Wednesday respectively and boat B traveled 50 km and 45 km downstream on Thursday and Friday respectively. Find the total time taken by both the boats.
a) 11 hr
b) 12 hr
c) 13 hr
d) 14 hr
e) 15 hr
3. If on Sunday, boat B traveled downstream with 20% more downstream speed than previous day and boat A traveled upstream with 25% more upstream speed than the previous day, what will be the ratio between upstream speed of boat A and downstream speed of boat B on Sunday?
a) 5: 12
b) 12: 5
c) 11: 17
d) 17: 11
e) None of these
4. If the sum of time taken by stream to travel in the direction of boat A and boat B for the same distance on Monday is 13 hours, what is the time taken by stream to travel in the direction of boat B on Wednesday for the same distance?
a) 4 hr 12 minutes
b) 4 hr 42 minutes
c) 5 hr
d) 6 hr
e) 6 hr 24 minutes
5. On Friday, the total distance traveled downstream by boat A and boat B is 310 km and time taken by boat A and boat B to travel downstream is in the ratio 4: 5. Find the average speed of boat A if the ratio of time taken by boat A to travel upstream and downstream on Friday is 3: 2.
a) 14 km/hr
b) 15.5 km/hr
c) 16.5 km/hr
d) 17 km/hr
e) None of these
Solution:

SSC CGL Quantitative Aptitude Questions – Important Algebra Questions

Q1) If x = 2 then the value of x3 + 27x2 + 243x + 631 is:

A. 1211
B. 1231
C. 1233
D. 1321

Q2) if x + 1/x = 99, find the value of 100x / (2x+ 102x + 2)

A. 1/6
B.1/2
C.1/3
D.1/4

SSC CGL Quantitative Aptitude Questions – Important Trigonometry Questions

Q1) If cosΘ = – 1/2 and π < Θ  < 3π, find the value of 4 tan2Θ – 3 cosec2Θ

A. 12
B. 8
C. 4
D. 2

Explanation:

B

We know that
sinΘ = ± 1 – cos2

or, sinΘ = 1-1/4 = 3/2

Since Θ lies in the third quadrant, the value of sinΘ is negative.
or, cosecΘ = -2/3

and tanΘ= sinΘ/cosΘ = 3

Since Θ lies in the third quadrant, the value of tanΘ is positive.] Now, 4 tan2Θ – 3 cosec2Θ = 4 × 3 – 3 × 4/3 = 8

Q2) If 8 sin x = 4 + cos x, the values of sin x are :

A. 3/5, -5/13
B. -3/5, 5/13
C. -3/5, -5/13
D.  3/5, 5/13

Explanation: 8 sin x – 4 = cos x ⇒ 8 sin x – 4 = 1- sin2 x

⇒ sin x = 3/5 or sin x = 5/13

⇒ 1 – sin2 x = (8 sin x – 4)2

⇒ 1 – sin2 x = 64 sin2 x + 16 – 64 sin x

⇒ 65 sin2 x – 64 sin x + 15 = 0

⇒ 65 sin2 x – 39 sin x  –  25 sin x + 15 = 0

⇒ 13 sin x (5 sin x  – 3)  –  5 (5 sin x  –  3) = 0

⇒ (5 sin x – 3) (13 sin x – 5) =0
therefore, sin x = 3/5 or 5/13

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SSC CGL Quantitative Aptitude Questions – Important Number System Important Questions

Q1) The sum of two numbers is 184. If one-third of the one exceeds one-seventh of the other by 8, find the smaller number.

A. 65
B. 68
C. 70
D. 72

Q2) Find a number such that when 15 is subtracted from 7 times the number, the result is 10 more than twice the number.

A. 5
B. 10
C. 15
D. 20

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SSC CGL Quantitative Aptitude Questions – Important Ratio and Proportion Questions

Q1) The ratio of efficiency of Q and R is 4: 5. When P works with 50% more efficiency than his actual efficiency, work is completed in 10 days less as compared to when he worked with 75% of his actual efficiency and when Q works with 50% less efficiency than his actual efficiency, work is completed in 30 days more as compared to when he worked with 25% more efficiency than his actual efficiency. Find the approximate time taken by P, Q, and R together to complete the whole work.

a) 5 hours 37 min
b) 6 hours 23 min
c) 7 hours 18 min
d) 8 hours 9 min
e) None of these

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SSC CGL Quantitative Aptitude Questions – Important Compound Interest and Simple Interest

Q1) A sum of 13300 is to be divided between Anshul, Karan and Rahul who are respectively 19, 20 and 21 years old in the ratio 5: 7: 7. Their shares are invested at a% per annum at simple interest and the sum of the amount received by them at the age of 25 years is 5208. What is the difference between compound interest when Karan and Anshul invested their shares for two years?

a) Rs.300
b) Rs.279.55
c) Rs.250
d) Rs.232.96
e) None of these

Q2)  P and Q have equal amounts. P invested half amount at 10% compound interest and remaining half at 6% simple interest for 2 years and Q invest amount at 20% compound interest and remaining amount at 10% simple interest for 2 years. If the total interest received by both P and Q is Rs.7540, find the sum.
a) Rs.12000
b) Rs.12500
c) Rs.13500
d) Rs.14000
e) None of these solutions:

SSC CGL Quantitative Aptitude Questions – Important Miscellaneous Questions

Q1) The radii of three cylinders A, B and C are in the ratio 2: 3: 4 and their heights are 20%, 25% and 30% more than the length, breadth and height of a wooden block whose sides are in the ratio 7: 5: 3. What is the ratio of the difference between the volumes of cylinders A and C to the sum of the volume of cylinders having the largest and shortest height?
a) 11: 43
b) 7: 22
c) 15: 29
d) 17: 63
e) None of these

Q2) A ration shopkeeper wants to make some profit by selling wheat. He tries various methods to earn profit. Which one of his methods would maximize his profit?

a) Selling wheat at a direct profit of 15%.
b) Selling wheat, using 800 gm instead of 1 kg.
c) Increasing the price of wheat by 6 %.
d) Adding some impurities of about 5% and decreasing the weights by 5 %.

A) a only.
B) b only .
C) a , b , c .
D) only c.
E) None of these

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Q3) A man take 30 days to reach the point c under normal conditions. But, due to the increase in the bad weather conditions, the distance is reduced by 30. How many days would a man take to reach the point c.

a) 25
b) 15
c) 20
d) none of the above

Q4) If A &amp; B work together, they will complete a job in 7.5 days. However if A works alone and completes half the job and the B takes over and completes the remaining half alone, they will be able to complete the job in 20 days. How long will B alone take to do the job if A is more efficient than B?

a 20
b 30
c 36
d 40

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Q5) (4.5 × 4.5 × 4.5 × 4.5) ÷ 225 ÷ 25 + 33 = ?

(a) 27.729
(b) 277.29
(c) 27.0729
(d) 2772.90

Q6) 38.4% of 1450 + 78.2% of 240 – ?2 = 20% of 77.4

(a) 19
(b) 27
(c) none of these
(d) 81

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