Q1. A's salary is 40% more than B's salary. By what percent is B's salary less than A's?
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Answer: C. 28 4/7%
Let B = 100, so A = 140. B is less by 40/140 × 100 = 28 4/7%.
SSC CGL Quantitative Aptitude Intermediate Practice Set 8
25 intermediate questions. Tap an option to check it, or open “Show answer” for the explanation.
Topics: Percentage, Simple Interest, Number System, Profit and Loss, Geometry, Discount, Problems on Ages, Average, Simplification, Time and Work, Ratio and Proportion, Mensuration, Speed, Time and Distance, Boats and Streams, LCM and HCF
Score: 0 / 0
Q2. At 8% per annum simple interest, a sum earns ₹1400 as interest in 5 years. Find the sum (in ₹).
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Answer: B. 3500
P = 1400 × 100 / (8 × 5) = ₹3500.
Q3. The price of an item rises from ₹500 to ₹625. What is the percentage increase?
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Answer: A. 25%
Increase = 625 − 500 = 125. % increase = 125/500 × 100 = 25%.
Q4. The population of a town is 55000. It increases by 20% every year. What will the population be after 2 years?
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Answer: C. 79200
55000 × (120/100)^2 = 79200.
Q5. How many factors (divisors) does 225 have?
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Answer: D. 9
225 = 3^2 × 5^2; number of factors = 3 × 3 = 9.
Q6. A shopkeeper buys a watch for ₹2000 and sells it for ₹2200. Find the profit or loss percentage.
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Answer: D. 10% profit
Profit = |2200 − 2000| = ₹200. Profit% = 200/2000 × 100 = 10%.
Q7. How many diagonals does a polygon with 16 sides have?
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Answer: D. 104
16 × 13/2 = 104.
Q8. The marked price of a shirt is ₹4500. A discount of 40% is given. What is the selling price (in ₹)?
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Answer: C. 2700
SP = 4500 × 60/100 = ₹2700.
Q9. The present ages of A and B are in the ratio 2:3. After 5 years, their ages will be in the ratio 11:14. What is A's present age?
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Answer: D. 6 years
14(2x + 5) = 11(3x + 5) ⇒ x = 3. A's age = 2 × 3 = 6 years.
Q10. A sum of ₹3000 amounts to ₹4800 in 5 years at simple interest. What is the rate of interest per annum?
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Answer: B. 12%
SI = 4800 − 3000 = ₹1800. R = 1800 × 100 / (3000 × 5) = 12%.
Q11. A batsman has an average of 50 runs after 13 innings. How many runs must he score in the next innings to raise his average by 1?
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Answer: C. 64
New total = 14 × 51 = 714; old total = 13 × 50 = 650. Runs = 64.
Q12. Find the value of 84² − 20².
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Answer: D. 6656
(84 + 20)(84 − 20) = 104 × 64 = 6656.
Q13. The present ages of A and B are in the ratio 2:3. After 4 years, their ages will be in the ratio 3:4. What is A's present age?
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Answer: C. 8 years
4(2x + 4) = 3(3x + 4) ⇒ x = 4. A's age = 2 × 4 = 8 years.
Q14. A's salary is 50% more than B's salary. By what percent is B's salary less than A's?
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Answer: B. 33 1/3%
Let B = 100, so A = 150. B is less by 50/150 × 100 = 33 1/3%.
Q15. The average age of 20 students in a class is 58 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: A. 79 years
Teacher's age = (20 + 1) × 59 − 20 × 58 = 1239 − 1160 = 79 years.
Q16. 28 men can complete a work in 10 days. In how many days can 5 men complete the same work?
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Answer: C. 56 days
28 × 10 = 5 × D ⇒ D = 280/5 = 56 days.
Q17. A, B and C can do a work alone in 15, 20 and 60 days respectively. How many days will they take working together?
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Answer: B. 7.5 days
1/15 + 1/20 + 1/60 = 1/7.5. So they need 7.5 days.
Q18. If A:B = 3:7 and B:C = 5:6, find A:B:C.
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Answer: D. 15:35:42
Multiply the first ratio by 5 and the second by 7: A:B:C = 15:35:42 = 15:35:42.
Q19. A, B and C can do a work alone in 20, 30 and 60 days respectively. How many days will they take working together?
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Answer: A. 10 days
1/20 + 1/30 + 1/60 = 1/10. So they need 10 days.
Q20. Find the volume of a sphere of radius 21 cm. (Take π = 22/7)
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Answer: B. 38808 cm³
V = 4/3 × 22/7 × 21³ = 38808 cm³.
Q21. Two cities are 420 km apart. Two cars start at the same time from the two cities towards each other at 22 km/h and 38 km/h. After how many hours will they meet?
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Answer: C. 7 hours
Time = 420/(22 + 38) = 7 hours.
Q22. A train 160 m long runs at 36 km/h. How long will it take to cross a platform 150 m long?
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Answer: B. 31 seconds
Speed = 36 × 5/18 = 10 m/s. Distance = 160 + 150 = 310 m. Time = 310/10 = 31 s.
Q23. A boat goes downstream at 16 km/h and upstream at 14 km/h. What is the speed of the stream?
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Answer: B. 1 km/h
(16 − 14)/2 = 1 km/h.
Q24. A boat goes downstream at 12 km/h and upstream at 8 km/h. What is the speed of the stream?
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Answer: D. 2 km/h
(12 − 8)/2 = 2 km/h.
Q25. What is the least number which, when divided by 9, 18 and 12, leaves a remainder of 1 in each case?
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Answer: A. 37
LCM(9, 18, 12) = 36. Required number = 36 + 1 = 37.