Q1. In what ratio must rice at ₹10/kg be mixed with rice at ₹20/kg so that the mixture costs ₹19/kg?
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Answer: C. 1:9
Ratio = (20 − 19) : (19 − 10) = 1:9.
SSC CGL Quantitative Aptitude Advanced Practice Set 6
25 advanced questions, suggested time 30 minutes. Tap an option to check it, or open “Show answer” for the explanation.
Topics: Mixture and Alligation, Partnership, Percentage, Profit and Loss, Compound Interest, Ratio and Proportion, Pipes and Cisterns, Speed, Time and Distance, LCM and HCF, Number System, Algebra, Problems on Ages, Simple Interest, Average, Trigonometry
Score: 0 / 0
Q2. A invests ₹30000 for 12 months and B invests ₹15000 for 8 months. Out of a total profit of ₹808, what is A's share (in ₹)?
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Answer: A. 606
Ratio = 30000×12 : 15000×8 = 3:1. A's share = 808 × 3/4 = ₹606.
Q3. The price of a commodity is first increased by 20% and then decreased by 20%. What is the net percentage change?
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Answer: B. 4% decrease
Net change = 20 − 20 − (20×20)/100 = -4%, i.e. a 4% decrease.
Q4. A trader marks an article at ₹2200 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: D. 1408
SP = 2200 × 80/100 = ₹1760. CP = 1760 × 100/125 = ₹1408.
Q5. What is the difference between compound interest and simple interest on ₹15500 for 2 years at 10% per annum (in ₹)?
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Answer: C. 155
CI − SI = 15500 × (10/100)² = ₹155.
Q6. Find the mean proportional between 162 and 36.
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Answer: C. 18
√(162 × 36) = √5832 = 18.
Q7. A pipe can fill a tank in 15 hours, while a leak can empty the full tank in 30 hours. If both are open, how long will it take to fill the tank?
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Answer: D. 30 hours
Net filled per hour = 1/15 − 1/30 = 15/450. Time = 450/15 = 30 hours.
Q8. A man travels from A to B at 60 km/h and returns at 90 km/h. What is his average speed for the whole journey?
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Answer: C. 72 km/h
Average speed = 2 × 60 × 90/(60 + 90) = 72 km/h.
Q9. The HCF of two numbers is 23 and their LCM is 483. If one of the numbers is 69, find the other.
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Answer: D. 161
Other number = (23 × 483) / 69 = 161.
Q10. What is the remainder when 7474 is divided by 13?
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Answer: B. 12
7474 = 13 × 574 + 12. Remainder = 12.
Q11. If x + 1/x = 6, find the value of x² + 1/x².
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Answer: B. 34
x² + 1/x² = 6² − 2 = 34.
Q12. A father's age is 5 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: D. 9 years
5x + 9 = 3x + 27 ⇒ 2x = 18 ⇒ x = 9 years.
Q13. In what ratio must rice at ₹15/kg be mixed with rice at ₹25/kg so that the mixture costs ₹16/kg?
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Answer: B. 9:1
Ratio = (25 − 16) : (16 − 15) = 9:1.
Q14. A invests ₹50000 for 8 months and B invests ₹40000 for 6 months. Out of a total profit of ₹8528, what is A's share (in ₹)?
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Answer: A. 5330
Ratio = 50000×8 : 40000×6 = 5:3. A's share = 8528 × 5/8 = ₹5330.
Q15. The price of a commodity is first increased by 30% and then decreased by 20%. What is the net percentage change?
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Answer: D. 4% increase
Net change = 30 − 20 − (30×20)/100 = 4%, i.e. a 4% increase.
Q16. A trader marks an article at ₹1400 and allows a discount of 25%. He still earns a profit of 20%. What is the cost price of the article (in ₹)?
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Answer: D. 875
SP = 1400 × 75/100 = ₹1050. CP = 1050 × 100/120 = ₹875.
Q17. In how many years will a sum of money become double itself at 4% per annum simple interest?
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Answer: A. 25 years
SI = 1P, so 1P = P × 4 × T / 100, giving T = 100/4 = 25 years.
Q18. What is the difference between compound interest and simple interest on ₹29500 for 2 years at 10% per annum (in ₹)?
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Answer: B. 295
CI − SI = 29500 × (10/100)² = ₹295.
Q19. The average of 9 consecutive even numbers is 60. What is the largest of these numbers?
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Answer: A. 68
The middle (5th) number is 60. The largest is 4 steps of 2 above it: 60 + 8 = 68.
Q20. Find the mean proportional between 567 and 441.
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Answer: C. 63
√(567 × 441) = √250047 = 63.
Q21. A pipe can fill a tank in 20 hours, while a leak can empty the full tank in 60 hours. If both are open, how long will it take to fill the tank?
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Answer: B. 30 hours
Net filled per hour = 1/20 − 1/60 = 40/1200. Time = 1200/40 = 30 hours.
Q22. A man travels from A to B at 20 km/h and returns at 30 km/h. What is his average speed for the whole journey?
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Answer: A. 24 km/h
Average speed = 2 × 20 × 30/(20 + 30) = 24 km/h.
Q23. The HCF of two numbers is 12 and their LCM is 120. If one of the numbers is 24, find the other.
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Answer: D. 60
Other number = (12 × 120) / 24 = 60.
Q24. What is the remainder when 6647 is divided by 13?
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Answer: B. 4
6647 = 13 × 511 + 4. Remainder = 4.
Q25. Find the value of cos 0° + sin 90° + tan 0°.
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Answer: C. 2
1 + 1 + 0 = 2.