Q1. The price of a commodity is first increased by 10% and then decreased by 20%. What is the net percentage change?
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Answer: B. 12% decrease
Net change = 10 − 20 − (10×20)/100 = -12%, i.e. a 12% decrease.
SSC CGL Quantitative Aptitude Advanced Practice Set 3
25 advanced questions, suggested time 30 minutes. Tap an option to check it, or open “Show answer” for the explanation.
Topics: Percentage, Profit and Loss, Discount, Simple Interest, Compound Interest, Average, Ratio and Proportion, Pipes and Cisterns, Speed, Time and Distance, LCM and HCF, Number System, Algebra, Problems on Ages, Mensuration, Trigonometry, Mixture and Alligation, Partnership
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Q2. A trader marks an article at ₹2400 and allows a discount of 10%. He still earns a profit of 8%. What is the cost price of the article (in ₹)?
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Answer: D. 2000
SP = 2400 × 90/100 = ₹2160. CP = 2160 × 100/108 = ₹2000.
Q3. Two successive discounts of 10% and 5% are equivalent to a single discount of:
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Answer: A. 14.5%
Equivalent = 10 + 5 − (10×5)/100 = 14.5%.
Q4. In how many years will a sum of money become three times itself at 8% per annum simple interest?
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Answer: A. 25 years
SI = 2P, so 2P = P × 8 × T / 100, giving T = 200/8 = 25 years.
Q5. What is the difference between compound interest and simple interest on ₹47500 for 2 years at 12% per annum (in ₹)?
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Answer: B. 684
CI − SI = 47500 × (12/100)² = ₹684.
Q6. The average of 5 consecutive even numbers is 84. What is the largest of these numbers?
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Answer: A. 88
The middle (3th) number is 84. The largest is 2 steps of 2 above it: 84 + 4 = 88.
Q7. Find the mean proportional between 32 and 128.
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Answer: A. 16
√(32 × 128) = √4096 = 16.
Q8. A pipe can fill a tank in 10 hours, while a leak can empty the full tank in 15 hours. If both are open, how long will it take to fill the tank?
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Answer: C. 30 hours
Net filled per hour = 1/10 − 1/15 = 5/150. Time = 150/5 = 30 hours.
Q9. A man travels from A to B at 36 km/h and returns at 45 km/h. What is his average speed for the whole journey?
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Answer: A. 40 km/h
Average speed = 2 × 36 × 45/(36 + 45) = 40 km/h.
Q10. The HCF of two numbers is 15 and their LCM is 150. If one of the numbers is 30, find the other.
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Answer: D. 75
Other number = (15 × 150) / 30 = 75.
Q11. What is the remainder when 7792 is divided by 11?
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Answer: C. 4
7792 = 11 × 708 + 4. Remainder = 4.
Q12. If x + 1/x = 5, find the value of x³ + 1/x³.
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Answer: B. 110
x³ + 1/x³ = 5³ − 3 × 5 = 125 − 15 = 110.
Q13. A father's age is 4 times his son's age. After 9 years, the father will be 3 times as old as his son. What is the son's present age?
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Answer: C. 18 years
4x + 9 = 3x + 27 ⇒ x = 18 ⇒ x = 18 years.
Q14. Find the volume of a cylinder with radius 7 cm and height 14 cm. (Take π = 22/7)
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Answer: B. 2156 cm³
V = 22/7 × 7² × 14 = 2156 cm³.
Q15. Find the value of cos² 45° − sin² 30°.
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Answer: B. 1/4
1/2 − 1/4 = 1/4.
Q16. In what ratio must rice at ₹12/kg be mixed with rice at ₹18/kg so that the mixture costs ₹16/kg?
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Answer: A. 1:2
Ratio = (18 − 16) : (16 − 12) = 2:4 = 1:2.
Q17. A invests ₹30000 for 12 months and B invests ₹40000 for 12 months. Out of a total profit of ₹6412, what is A's share (in ₹)?
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Answer: B. 2748
Ratio = 30000×12 : 40000×12 = 3:4. A's share = 6412 × 3/7 = ₹2748.
Q18. The price of a commodity is first increased by 10% and then decreased by 10%. What is the net percentage change?
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Answer: A. 1% decrease
Net change = 10 − 10 − (10×10)/100 = -1%, i.e. a 1% decrease.
Q19. A trader marks an article at ₹2800 and allows a discount of 20%. He still earns a profit of 25%. What is the cost price of the article (in ₹)?
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Answer: C. 1792
SP = 2800 × 80/100 = ₹2240. CP = 2240 × 100/125 = ₹1792.
Q20. Two successive discounts of 30% and 10% are equivalent to a single discount of:
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Answer: A. 37%
Equivalent = 30 + 10 − (30×10)/100 = 37%.
Q21. In how many years will a sum of money become double itself at 5% per annum simple interest?
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Answer: B. 20 years
SI = 1P, so 1P = P × 5 × T / 100, giving T = 100/5 = 20 years.
Q22. What is the difference between compound interest and simple interest on ₹26500 for 2 years at 20% per annum (in ₹)?
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Answer: A. 1060
CI − SI = 26500 × (20/100)² = ₹1060.
Q23. The average of 11 consecutive even numbers is 40. What is the largest of these numbers?
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Answer: A. 50
The middle (6th) number is 40. The largest is 5 steps of 2 above it: 40 + 10 = 50.
Q24. Find the mean proportional between 441 and 567.
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Answer: C. 63
√(441 × 567) = √250047 = 63.
Q25. A man travels from A to B at 45 km/h and returns at 90 km/h. What is his average speed for the whole journey?
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Answer: A. 60 km/h
Average speed = 2 × 45 × 90/(45 + 90) = 60 km/h.