Q1. The population of a town is 90000. It increases by 20% every year. What will the population be after 2 years?
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Answer: A. 129600
90000 × (120/100)^2 = 129600.
SSC CGL Quantitative Aptitude Intermediate Practice Set 10
25 intermediate questions. Tap an option to check it, or open “Show answer” for the explanation.
Topics: Percentage, Number System, Discount, Geometry, Simple Interest, Problems on Ages, Average, Simplification, Ratio and Proportion, Time and Work, Mensuration, Speed, Time and Distance, LCM and HCF, Boats and Streams, Statistics, Algebra
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Q2. How many factors (divisors) does 72 have?
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Answer: D. 12
72 = 2^3 × 3^2; number of factors = 4 × 3 = 12.
Q3. The marked price of a shirt is ₹3500. A discount of 30% is given. What is the selling price (in ₹)?
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Answer: B. 2450
SP = 3500 × 70/100 = ₹2450.
Q4. How many diagonals does a polygon with 8 sides have?
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Answer: B. 20
8 × 5/2 = 20.
Q5. A sum of ₹13500 amounts to ₹15120 in 2 years at simple interest. What is the rate of interest per annum?
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Answer: C. 6%
SI = 15120 − 13500 = ₹1620. R = 1620 × 100 / (13500 × 2) = 6%.
Q6. At 12% per annum simple interest, a sum earns ₹1260 as interest in 3 years. Find the sum (in ₹).
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Answer: A. 3500
P = 1260 × 100 / (12 × 3) = ₹3500.
Q7. The present ages of A and B are in the ratio 2:9. After 12 years, their ages will be in the ratio 6:13. What is A's present age?
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Answer: B. 6 years
13(2x + 12) = 6(9x + 12) ⇒ x = 3. A's age = 2 × 3 = 6 years.
Q8. A batsman has an average of 53 runs after 18 innings. How many runs must he score in the next innings to raise his average by 1?
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Answer: C. 72
New total = 19 × 54 = 1026; old total = 18 × 53 = 954. Runs = 72.
Q9. Find the value of 59² − 41².
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Answer: D. 1800
(59 + 41)(59 − 41) = 100 × 18 = 1800.
Q10. The average age of 10 students in a class is 22 years. When the teacher's age is included, the average increases by 1 year. What is the teacher's age?
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Answer: C. 33 years
Teacher's age = (10 + 1) × 23 − 10 × 22 = 253 − 220 = 33 years.
Q11. The present ages of A and B are in the ratio 3:7. After 8 years, their ages will be in the ratio 7:11. What is A's present age?
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Answer: B. 6 years
11(3x + 8) = 7(7x + 8) ⇒ x = 2. A's age = 3 × 2 = 6 years.
Q12. If A:B = 7:6 and B:C = 2:3, find A:B:C.
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Answer: D. 7:6:9
Multiply the first ratio by 2 and the second by 6: A:B:C = 14:12:18 = 7:6:9.
Q13. 30 men can complete a work in 28 days. In how many days can 8 men complete the same work?
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Answer: A. 105 days
30 × 28 = 8 × D ⇒ D = 840/8 = 105 days.
Q14. A, B and C can do a work alone in 12, 24 and 24 days respectively. How many days will they take working together?
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Answer: D. 6 days
1/12 + 1/24 + 1/24 = 1/6. So they need 6 days.
Q15. A, B and C can do a work alone in 18, 24 and 72 days respectively. How many days will they take working together?
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Answer: C. 9 days
1/18 + 1/24 + 1/72 = 1/9. So they need 9 days.
Q16. Find the volume of a cone with base radius 7 cm and height 7 cm. (Take π = 22/7)
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Answer: B. 359 1/3 cm³
V = 1/3 × 22/7 × 7² × 7 = 359 1/3 cm³.
Q17. A train 200 m long runs at 90 km/h. How long will it take to cross a platform 350 m long?
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Answer: A. 22 seconds
Speed = 90 × 5/18 = 25 m/s. Distance = 200 + 350 = 550 m. Time = 550/25 = 22 s.
Q18. Two cities are 390 km apart. Two cars start at the same time from the two cities towards each other at 35 km/h and 30 km/h. After how many hours will they meet?
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Answer: D. 6 hours
Time = 390/(35 + 30) = 6 hours.
Q19. What is the least number which, when divided by 6, 15 and 30, leaves a remainder of 5 in each case?
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Answer: A. 35
LCM(6, 15, 30) = 30. Required number = 30 + 5 = 35.
Q20. A boat goes downstream at 27 km/h and upstream at 15 km/h. What is the speed of the stream?
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Answer: A. 6 km/h
(27 − 15)/2 = 6 km/h.
Q21. A boat goes downstream at 14 km/h and upstream at 12 km/h. What is the speed of the stream?
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Answer: C. 1 km/h
(14 − 12)/2 = 1 km/h.
Q22. What is the unit digit of 3^38?
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Answer: D. 9
Unit digits of 3^1, ^2, ^3, ^4 are 3, 9, 7, 1. 38 leaves remainder 2 on division by 4, so take the 2nd value in the cycle: 9.
Q23. How many factors (divisors) does 360 have?
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Answer: B. 24
360 = 2^3 × 3^2 × 5; number of factors = 4 × 3 × 2 = 24.
Q24. Find the median of: 22, 36, 55, 53, 56, 35, 31, 32, 43.
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Answer: C. 36
In order: 22, 31, 32, 35, 36, 43, 53, 55, 56. Median = 36.
Q25. If a + b = 7 and ab = 15, find a² + b².
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Answer: C. 19
a² + b² = (a + b)² − 2ab = 49 − 30 = 19.