Q1. A's salary is 60% more than B's salary. By what percent is B's salary less than A's?
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Answer: D. 37.5%
Let B = 100, so A = 160. B is less by 60/160 × 100 = 37.5%.
SSC CGL Quantitative Aptitude Advanced Practice Set 10
25 advanced questions, suggested time 30 minutes. Tap an option to check it, or open “Show answer” for the explanation.
Topics: Percentage, Compound Interest, Indices and Surds, Profit and Loss, Speed, Time and Distance, Average, Boats and Streams, Problems on Ages, Time and Work, Trigonometry, Ratio and Proportion, Pipes and Cisterns, Mensuration, Number System
Score: 0 / 0
Q2. Find the compound interest on ₹40000 for 1 year at 10% per annum, compounded half-yearly (in ₹).
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Answer: C. 4100
Rate = 5% per half-year for 2 periods. A = 40000 × (105/100)² = ₹44100; CI = ₹4100.
Q3. The population of a town is 10000. It increases by 10% every year. What will the population be after 2 years?
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Answer: C. 12100
10000 × (110/100)^2 = 12100.
Q4. Find the value of (3^8 × 3^8) ÷ 3^5.
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Answer: D. 177147
3^(8 + 8 − 5) = 3^11 = 177147.
Q5. A trader marks an article at ₹600 and allows a discount of 10%. He still earns a profit of 20%. What is the cost price of the article (in ₹)?
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Answer: C. 450
SP = 600 × 90/100 = ₹540. CP = 540 × 100/120 = ₹450.
Q6. An article is sold at a loss of 10%. Had it been sold for ₹60 more, there would have been a gain of 10%. Find the cost price (in ₹).
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Answer: C. 300
10% + 10% = 20% of CP = ₹60, so CP = 60 × 100/20 = ₹300.
Q7. The population of a town is 65000. It increases by 20% every year. What will the population be after 3 years?
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Answer: A. 112320
65000 × (120/100)^3 = 112320.
Q8. Find the compound interest on ₹40000 for 1 year at 20% per annum, compounded half-yearly (in ₹).
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Answer: C. 8400
Rate = 10% per half-year for 2 periods. A = 40000 × (110/100)² = ₹48400; CI = ₹8400.
Q9. Two cities are 450 km apart. Two cars start at the same time from the two cities towards each other at 40 km/h and 20 km/h. After how many hours will they meet?
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Answer: D. 7.5 hours
Time = 450/(40 + 20) = 7.5 hours.
Q10. A batsman has an average of 55 runs after 13 innings. How many runs must he score in the next innings to raise his average by 4?
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Answer: C. 111
New total = 14 × 59 = 826; old total = 13 × 55 = 715. Runs = 111.
Q11. A boat goes downstream at 11 km/h and upstream at 1 km/h. What is the speed of the stream?
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Answer: D. 5 km/h
(11 − 1)/2 = 5 km/h.
Q12. What is the difference between compound interest and simple interest on ₹9000 for 2 years at 20% per annum (in ₹)?
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Answer: D. 360
CI − SI = 9000 × (20/100)² = ₹360.
Q13. The present ages of A and B are in the ratio 2:9. After 12 years, their ages will be in the ratio 8:15. What is A's present age?
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Answer: C. 4 years
15(2x + 12) = 8(9x + 12) ⇒ x = 2. A's age = 2 × 2 = 4 years.
Q14. A, B and C can do a work alone in 6, 12 and 12 days respectively. How many days will they take working together?
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Answer: D. 3 days
1/6 + 1/12 + 1/12 = 1/3. So they need 3 days.
Q15. The average of 5 consecutive even numbers is 42. What is the largest of these numbers?
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Answer: C. 46
The middle (3th) number is 42. The largest is 2 steps of 2 above it: 42 + 4 = 46.
Q16. If tan θ = 9/40 (θ acute), find sec θ.
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Answer: B. 41/40
Hypotenuse = √(9² + 40²) = 41. sec θ = 41/40.
Q17. Find the mean proportional between 384 and 288.
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Answer: C. 48
√(384 × 288) = √110592 = 48.
Q18. Two trains of lengths 250 m and 110 m run in the same direction at 36 km/h and 54 km/h. How long will they take to cross each other completely?
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Answer: A. 72 seconds
Relative speed = 18 km/h = 5 m/s. Time = (250 + 110)/5 = 72 s.
Q19. A batsman has an average of 43 runs after 20 innings. How many runs must he score in the next innings to raise his average by 3?
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Answer: A. 106
New total = 21 × 46 = 966; old total = 20 × 43 = 860. Runs = 106.
Q20. A pipe can fill a tank in 4 hours, while a leak can empty the full tank in 12 hours. If both are open, how long will it take to fill the tank?
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Answer: C. 6 hours
Net filled per hour = 1/4 − 1/12 = 8/48. Time = 48/8 = 6 hours.
Q21. Two cities are 270 km apart. Two cars start at the same time from the two cities towards each other at 24 km/h and 36 km/h. After how many hours will they meet?
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Answer: A. 4.5 hours
Time = 270/(24 + 36) = 4.5 hours.
Q22. Find the volume of a cone with base radius 7 cm and height 20 cm. (Take π = 22/7)
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Answer: C. 1026 2/3 cm³
V = 1/3 × 22/7 × 7² × 20 = 1026 2/3 cm³.
Q23. The speed of a boat in still water is 10 km/h and the speed of the stream is 2 km/h. How long will the boat take to go 32 km upstream?
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Answer: A. 4 hours
Upstream speed = 10 − 2 = 8 km/h. Time = 32/8 = 4 hours.
Q24. How many factors (divisors) does 200 have?
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Answer: D. 12
200 = 2^3 × 5^2; number of factors = 4 × 3 = 12.
Q25. An article is sold at a loss of 4%. Had it been sold for ₹290 more, there would have been a gain of 6%. Find the cost price (in ₹).
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Answer: D. 2900
4% + 6% = 10% of CP = ₹290, so CP = 290 × 100/10 = ₹2900.