Q1. What is the remainder when 9026 is divided by 11?
Show answer
Answer: D. 6
9026 = 11 × 820 + 6. Remainder = 6.
SSC CGL Quantitative Aptitude Advanced Practice Set 8
25 advanced questions, suggested time 30 minutes. Tap an option to check it, or open “Show answer” for the explanation.
Topics: Number System, Mensuration, Speed, Time and Distance, Problems on Ages, Trigonometry, Geometry, Boats and Streams, Compound Interest, Partnership, Percentage, Indices and Surds, Profit and Loss, Average, Time and Work
Score: 0 / 0
Q2. Find the total surface area of a solid hemisphere of radius 21 cm. (Take π = 22/7)
Show answer
Answer: B. 4158 cm²
TSA = 3 × 22/7 × 21² = 4158 cm².
Q3. If each side of a square is increased by 50%, by what percent does its area increase?
Show answer
Answer: C. 125%
Increase = 2 × 50 + 50²/100 = 125%.
Q4. Two trains of lengths 220 m and 140 m run in the same direction at 45 km/h and 36 km/h. How long will they take to cross each other completely?
Show answer
Answer: D. 144 seconds
Relative speed = 9 km/h = 2.5 m/s. Time = (220 + 140)/2.5 = 144 s.
Q5. A father is 2 times as old as his son. If the son is 20 years old, what will the father's age be after 2 years?
Show answer
Answer: C. 42 years
Father's present age = 2 × 20 = 40. After 2 years: 42 years.
Q6. If tan θ = 35/12 (θ acute), find cos θ.
Show answer
Answer: C. 12/37
Hypotenuse = √(35² + 12²) = 37. cos θ = 12/37.
Q7. How many diagonals does a polygon with 5 sides have?
Show answer
Answer: C. 5
5 × 2/2 = 5.
Q8. Find the volume of a cylinder with radius 7 cm and height 16 cm. (Take π = 22/7)
Show answer
Answer: A. 2464 cm³
V = 22/7 × 7² × 16 = 2464 cm³.
Q9. How many diagonals does a polygon with 9 sides have?
Show answer
Answer: C. 27
9 × 6/2 = 27.
Q10. The present ages of A and B are in the ratio 5:6. After 9 years, their ages will be in the ratio 13:15. What is A's present age?
Show answer
Answer: D. 30 years
15(5x + 9) = 13(6x + 9) ⇒ x = 6. A's age = 5 × 6 = 30 years.
Q11. A boat goes downstream at 10 km/h and upstream at 4 km/h. What is the speed of the stream?
Show answer
Answer: C. 3 km/h
(10 − 4)/2 = 3 km/h.
Q12. The diagonals of a rhombus are 28 cm and 15 cm. Find its area.
Show answer
Answer: B. 210 cm²
½ × 28 × 15 = 210 cm².
Q13. Find the compound interest on ₹24000 for 1 year at 10% per annum, compounded half-yearly (in ₹).
Show answer
Answer: B. 2460
Rate = 5% per half-year for 2 periods. A = 24000 × (105/100)² = ₹26460; CI = ₹2460.
Q14. A invests ₹20000 for 9 months and B invests ₹15000 for 6 months. Out of a total profit of ₹3837, what is A's share (in ₹)?
Show answer
Answer: B. 2558
Ratio = 20000×9 : 15000×6 = 2:1. A's share = 3837 × 2/3 = ₹2558.
Q15. The population of a town is 80000. It increases by 5% every year. What will the population be after 2 years?
Show answer
Answer: A. 88200
80000 × (105/100)^2 = 88200.
Q16. Find the value of (3^7 × 3^6) ÷ 3^3.
Show answer
Answer: C. 59049
3^(7 + 6 − 3) = 3^10 = 59049.
Q17. An article is sold at a loss of 8%. Had it been sold for ₹100 more, there would have been a gain of 12%. Find the cost price (in ₹).
Show answer
Answer: C. 500
8% + 12% = 20% of CP = ₹100, so CP = 100 × 100/20 = ₹500.
Q18. The population of a town is 50000. It increases by 20% every year. What will the population be after 3 years?
Show answer
Answer: B. 86400
50000 × (120/100)^3 = 86400.
Q19. A trader marks an article at ₹800 and allows a discount of 10%. He still earns a profit of 20%. What is the cost price of the article (in ₹)?
Show answer
Answer: C. 600
SP = 800 × 90/100 = ₹720. CP = 720 × 100/120 = ₹600.
Q20. Find the compound interest on ₹16000 for 1 year at 10% per annum, compounded half-yearly (in ₹).
Show answer
Answer: A. 1640
Rate = 5% per half-year for 2 periods. A = 16000 × (105/100)² = ₹17640; CI = ₹1640.
Q21. Two cities are 450 km apart. Two cars start at the same time from the two cities towards each other at 42 km/h and 48 km/h. After how many hours will they meet?
Show answer
Answer: C. 5 hours
Time = 450/(42 + 48) = 5 hours.
Q22. A batsman has an average of 52 runs after 14 innings. How many runs must he score in the next innings to raise his average by 1?
Show answer
Answer: B. 67
New total = 15 × 53 = 795; old total = 14 × 52 = 728. Runs = 67.
Q23. A boat goes downstream at 10 km/h and upstream at 8 km/h. What is the speed of the stream?
Show answer
Answer: C. 1 km/h
(10 − 8)/2 = 1 km/h.
Q24. The present ages of A and B are in the ratio 4:7. After 4 years, their ages will be in the ratio 2:3. What is A's present age?
Show answer
Answer: C. 8 years
3(4x + 4) = 2(7x + 4) ⇒ x = 2. A's age = 4 × 2 = 8 years.
Q25. A, B and C can do a work alone in 10, 12 and 15 days respectively. How many days will they take working together?
Show answer
Answer: D. 4 days
1/10 + 1/12 + 1/15 = 1/4. So they need 4 days.