Q1. What is the difference between compound interest and simple interest on ₹32500 for 2 years at 12% per annum (in ₹)?
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Answer: B. 468
CI − SI = 32500 × (12/100)² = ₹468.
SSC CGL Quantitative Aptitude Advanced Practice Set 9
25 advanced questions, suggested time 30 minutes. Tap an option to check it, or open “Show answer” for the explanation.
Topics: Compound Interest, Trigonometry, Average, Speed, Time and Distance, Mensuration, Profit and Loss, Indices and Surds, Number System, LCM and HCF, Geometry, Problems on Ages, Boats and Streams, Percentage, Partnership
Score: 0 / 0
Q2. If tan θ = 35/12 (θ acute), find sin θ.
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Answer: A. 35/37
Hypotenuse = √(35² + 12²) = 37. sin θ = 35/37.
Q3. The average of 7 consecutive even numbers is 62. What is the largest of these numbers?
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Answer: C. 68
The middle (4th) number is 62. The largest is 3 steps of 2 above it: 62 + 6 = 68.
Q4. Two trains of lengths 110 m and 170 m run in opposite directions at 60 km/h and 108 km/h. How long will they take to cross each other completely?
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Answer: D. 6 seconds
Relative speed = 168 km/h = 46 2/3 m/s. Time = (110 + 170)/46 2/3 = 6 s.
Q5. A batsman has an average of 37 runs after 14 innings. How many runs must he score in the next innings to raise his average by 4?
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Answer: D. 97
New total = 15 × 41 = 615; old total = 14 × 37 = 518. Runs = 97.
Q6. Two cities are 120 km apart. Two cars start at the same time from the two cities towards each other at 68 km/h and 28 km/h. After how many hours will they meet?
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Answer: A. 1.25 hours
Time = 120/(68 + 28) = 1.25 hours.
Q7. Find the total surface area of a cuboid of length 3 cm, breadth 5 cm and height 5 cm.
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Answer: B. 110 cm²
2(15 + 25 + 15) = 110 cm².
Q8. An article is sold at a loss of 12%. Had it been sold for ₹230 more, there would have been a gain of 8%. Find the cost price (in ₹).
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Answer: D. 1150
12% + 8% = 20% of CP = ₹230, so CP = 230 × 100/20 = ₹1150.
Q9. Find the value of (3^9 × 3^6) ÷ 3^6.
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Answer: B. 19683
3^(9 + 6 − 6) = 3^9 = 19683.
Q10. How many factors (divisors) does 196 have?
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Answer: B. 9
196 = 2^2 × 7^2; number of factors = 3 × 3 = 9.
Q11. The HCF of two numbers is 5 and their LCM is 105. If one of the numbers is 35, find the other.
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Answer: B. 15
Other number = (5 × 105) / 35 = 15.
Q12. Find the total surface area of a cuboid of length 16 cm, breadth 4 cm and height 8 cm.
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Answer: B. 448 cm²
2(64 + 32 + 128) = 448 cm².
Q13. What is the remainder when 5038 is divided by 11?
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Answer: C. 0
5038 = 11 × 458 + 0. Remainder = 0.
Q14. Two trains of lengths 250 m and 130 m run in the same direction at 45 km/h and 36 km/h. How long will they take to cross each other completely?
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Answer: C. 152 seconds
Relative speed = 9 km/h = 2.5 m/s. Time = (250 + 130)/2.5 = 152 s.
Q15. If tan θ = 12/5 (θ acute), find sec θ.
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Answer: D. 13/5
Hypotenuse = √(12² + 5²) = 13. sec θ = 13/5.
Q16. How many diagonals does a polygon with 12 sides have?
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Answer: B. 54
12 × 9/2 = 54.
Q17. A father's age is 5 times his son's age. After 3 years, the father will be 4 times as old as his son. What is the son's present age?
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Answer: B. 9 years
5x + 3 = 4x + 12 ⇒ x = 9 ⇒ x = 9 years.
Q18. The present ages of A and B are in the ratio 7:8. After 2 years, their ages will be in the ratio 8:9. What is A's present age?
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Answer: A. 14 years
9(7x + 2) = 8(8x + 2) ⇒ x = 2. A's age = 7 × 2 = 14 years.
Q19. Find the volume of a cylinder with radius 14 cm and height 18 cm. (Take π = 22/7)
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Answer: B. 11088 cm³
V = 22/7 × 14² × 18 = 11088 cm³.
Q20. A boat goes downstream at 27 km/h and upstream at 23 km/h. What is the speed of the stream?
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Answer: A. 2 km/h
(27 − 23)/2 = 2 km/h.
Q21. The diagonals of a rhombus are 56 cm and 14 cm. Find its area.
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Answer: A. 392 cm²
½ × 56 × 14 = 392 cm².
Q22. Find the compound interest on ₹16000 for 1 year at 20% per annum, compounded half-yearly (in ₹).
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Answer: D. 3360
Rate = 10% per half-year for 2 periods. A = 16000 × (110/100)² = ₹19360; CI = ₹3360.
Q23. The population of a town is 70000. It increases by 5% every year. What will the population be after 2 years?
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Answer: C. 77175
70000 × (105/100)^2 = 77175.
Q24. Find the value of (5^5 × 5^4) ÷ 5^3.
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Answer: B. 15625
5^(5 + 4 − 3) = 5^6 = 15625.
Q25. A invests ₹25000 for 6 months and B invests ₹35000 for 12 months. Out of a total profit of ₹26562, what is A's share (in ₹)?
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Answer: D. 6990
Ratio = 25000×6 : 35000×12 = 5:14. A's share = 26562 × 5/19 = ₹6990.