Q1. Find the compound interest on ₹8000 for 1 year at 10% per annum, compounded half-yearly (in ₹).
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Answer: B. 820
Rate = 5% per half-year for 2 periods. A = 8000 × (105/100)² = ₹8820; CI = ₹820.
SSC CGL Quantitative Aptitude Advanced Practice Set 7
25 advanced questions, suggested time 30 minutes. Tap an option to check it, or open “Show answer” for the explanation.
Topics: Compound Interest, Indices and Surds, Profit and Loss, Percentage, Speed, Time and Distance, Simple Interest, Average, Boats and Streams, Problems on Ages, Time and Work, Trigonometry, Ratio and Proportion, Mensuration, LCM and HCF, Number System
Score: 0 / 0
Q2. Find the value of (3^5 × 3^4) ÷ 3^3.
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Answer: A. 729
3^(5 + 4 − 3) = 3^6 = 729.
Q3. A trader marks an article at ₹2200 and allows a discount of 25%. He still earns a profit of 25%. What is the cost price of the article (in ₹)?
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Answer: D. 1320
SP = 2200 × 75/100 = ₹1650. CP = 1650 × 100/125 = ₹1320.
Q4. An article is sold at a loss of 10%. Had it been sold for ₹110 more, there would have been a gain of 10%. Find the cost price (in ₹).
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Answer: A. 550
10% + 10% = 20% of CP = ₹110, so CP = 110 × 100/20 = ₹550.
Q5. The population of a town is 40000. It increases by 5% every year. What will the population be after 2 years?
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Answer: B. 44100
40000 × (105/100)^2 = 44100.
Q6. Find the compound interest on ₹32000 for 1 year at 20% per annum, compounded half-yearly (in ₹).
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Answer: B. 6720
Rate = 10% per half-year for 2 periods. A = 32000 × (110/100)² = ₹38720; CI = ₹6720.
Q7. Two cities are 150 km apart. Two cars start at the same time from the two cities towards each other at 35 km/h and 25 km/h. After how many hours will they meet?
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Answer: D. 2.5 hours
Time = 150/(35 + 25) = 2.5 hours.
Q8. In how many years will a sum of money become three times itself at 5% per annum simple interest?
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Answer: C. 40 years
SI = 2P, so 2P = P × 5 × T / 100, giving T = 200/5 = 40 years.
Q9. A batsman has an average of 39 runs after 17 innings. How many runs must he score in the next innings to raise his average by 2?
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Answer: B. 75
New total = 18 × 41 = 738; old total = 17 × 39 = 663. Runs = 75.
Q10. A boat goes downstream at 25 km/h and upstream at 21 km/h. What is the speed of the stream?
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Answer: B. 2 km/h
(25 − 21)/2 = 2 km/h.
Q11. What is the difference between compound interest and simple interest on ₹37500 for 2 years at 4% per annum (in ₹)?
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Answer: C. 60
CI − SI = 37500 × (4/100)² = ₹60.
Q12. The present ages of A and B are in the ratio 2:7. After 6 years, their ages will be in the ratio 1:2. What is A's present age?
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Answer: A. 4 years
2(2x + 6) = 1(7x + 6) ⇒ x = 2. A's age = 2 × 2 = 4 years.
Q13. A, B and C can do a work alone in 6, 10 and 15 days respectively. How many days will they take working together?
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Answer: D. 3 days
1/6 + 1/10 + 1/15 = 1/3. So they need 3 days.
Q14. The average of 7 consecutive even numbers is 50. What is the largest of these numbers?
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Answer: B. 56
The middle (4th) number is 50. The largest is 3 steps of 2 above it: 50 + 6 = 56.
Q15. A, B and C can do a work alone in 10, 15 and 30 days respectively. How many days will they take working together?
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Answer: B. 5 days
1/10 + 1/15 + 1/30 = 1/5. So they need 5 days.
Q16. If tan θ = 5/12 (θ acute), find cos θ.
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Answer: D. 12/13
Hypotenuse = √(5² + 12²) = 13. cos θ = 12/13.
Q17. Find the mean proportional between 36 and 48.
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Answer: A. 12
√(36 × 48) = √1728 = 12.
Q18. Two trains of lengths 150 m and 130 m run in the same direction at 36 km/h and 45 km/h. How long will they take to cross each other completely?
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Answer: A. 112 seconds
Relative speed = 9 km/h = 2.5 m/s. Time = (150 + 130)/2.5 = 112 s.
Q19. A batsman has an average of 39 runs after 19 innings. How many runs must he score in the next innings to raise his average by 3?
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Answer: D. 99
New total = 20 × 42 = 840; old total = 19 × 39 = 741. Runs = 99.
Q20. Two cities are 480 km apart. Two cars start at the same time from the two cities towards each other at 51 km/h and 29 km/h. After how many hours will they meet?
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Answer: B. 6 hours
Time = 480/(51 + 29) = 6 hours.
Q21. Find the total surface area of a cuboid of length 6 cm, breadth 10 cm and height 5 cm.
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Answer: C. 280 cm²
2(60 + 50 + 30) = 280 cm².
Q22. An article is sold at a loss of 4%. Had it been sold for ₹240 more, there would have been a gain of 6%. Find the cost price (in ₹).
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Answer: C. 2400
4% + 6% = 10% of CP = ₹240, so CP = 240 × 100/10 = ₹2400.
Q23. The HCF of two numbers is 7 and their LCM is 70. If one of the numbers is 14, find the other.
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Answer: B. 35
Other number = (7 × 70) / 14 = 35.
Q24. Find the value of (5^8 × 5^5) ÷ 5^5.
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Answer: C. 390625
5^(8 + 5 − 5) = 5^8 = 390625.
Q25. How many factors (divisors) does 24 have?
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Answer: A. 8
24 = 2^3 × 3; number of factors = 4 × 2 = 8.