Q1. A and B together can finish a job in 12 days. A alone can finish it in 20 days. How many days will B alone take?
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Answer: C. 30 days
B's work per day = 1/12 − 1/20 = 1/30. So B alone takes 30 days.
SSC CGL Quantitative Aptitude Intermediate Practice Set 6
25 intermediate questions. Tap an option to check it, or open “Show answer” for the explanation.
Topics: Time and Work, Speed, Time and Distance, LCM and HCF, Number System, Algebra, Problems on Ages, Mensuration, Mixture and Alligation, Partnership, Simplification, Percentage, Profit and Loss, Discount, Simple Interest, Compound Interest, Average, Ratio and Proportion
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Q2. A train 280 m long runs at 36 km/h. How long will it take to cross a platform 350 m long?
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Answer: C. 63 seconds
Speed = 36 × 5/18 = 10 m/s. Distance = 280 + 350 = 630 m. Time = 630/10 = 63 s.
Q3. What is the least number which, when divided by 25, 16 and 10, leaves a remainder of 1 in each case?
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Answer: D. 401
LCM(25, 16, 10) = 400. Required number = 400 + 1 = 401.
Q4. What is the unit digit of 4^83?
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Answer: B. 4
Unit digits of 4^1, ^2, ^3, ^4 are 4, 6, 4, 6. 83 leaves remainder 3 on division by 4, so take the 3rd value in the cycle: 4.
Q5. If a + b = 8 and ab = 16, find a² + b².
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Answer: C. 32
a² + b² = (a + b)² − 2ab = 64 − 32 = 32.
Q6. A father's age is 5 times his son's age. After 15 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. 15 years
5x + 15 = 3x + 45 ⇒ 2x = 30 ⇒ x = 15 years.
Q7. Find the area of a circle of radius 42 cm. (Take π = 22/7)
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Answer: B. 5544 cm²
Area = 22/7 × 42 × 42 = 5544 cm².
Q8. In what ratio must rice at ₹30/kg be mixed with rice at ₹50/kg so that the mixture costs ₹48/kg?
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Answer: A. 1:9
Ratio = (50 − 48) : (48 − 30) = 2:18 = 1:9.
Q9. A invests ₹15000 for 12 months and B invests ₹40000 for 4 months. Out of a total profit of ₹24565, what is A's share (in ₹)?
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Answer: C. 13005
Ratio = 15000×12 : 40000×4 = 9:8. A's share = 24565 × 9/17 = ₹13005.
Q10. Find the value of √1681 + 7².
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Answer: D. 90
√1681 = 41; 7² = 49; total = 90.
Q11. The price of an item rises from ₹400 to ₹600. What is the percentage increase?
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Answer: B. 50%
Increase = 600 − 400 = 200. % increase = 200/400 × 100 = 50%.
Q12. A shopkeeper buys a watch for ₹2000 and sells it for ₹1800. Find the profit or loss percentage.
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Answer: B. 10% loss
Loss = |1800 − 2000| = ₹200. Loss% = 200/2000 × 100 = 10%.
Q13. The marked price of a shirt is ₹6000. A discount of 25% is given. What is the selling price (in ₹)?
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Answer: C. 4500
SP = 6000 × 75/100 = ₹4500.
Q14. A sum of ₹8500 amounts to ₹14875 in 5 years at simple interest. What is the rate of interest per annum?
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Answer: A. 15%
SI = 14875 − 8500 = ₹6375. R = 6375 × 100 / (8500 × 5) = 15%.
Q15. Find the compound interest on ₹20000 for 2 years at 20% per annum, compounded annually (in ₹).
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Answer: C. 8800
Amount = 20000 × (120/100)² = ₹28800. CI = 28800 − 20000 = ₹8800.
Q16. The average age of 20 students in a class is 60 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: B. 81 years
Teacher's age = (20 + 1) × 61 − 20 × 60 = 1281 − 1200 = 81 years.
Q17. If A:B = 4:3 and B:C = 5:3, find A:B:C.
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Answer: B. 20:15:9
Multiply the first ratio by 5 and the second by 3: A:B:C = 20:15:9 = 20:15:9.
Q18. A and B together can finish a job in 8 days. A alone can finish it in 10 days. How many days will B alone take?
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Answer: B. 40 days
B's work per day = 1/8 − 1/10 = 1/40. So B alone takes 40 days.
Q19. A train 240 m long runs at 72 km/h. How long will it take to cross a platform 400 m long?
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Answer: A. 32 seconds
Speed = 72 × 5/18 = 20 m/s. Distance = 240 + 400 = 640 m. Time = 640/20 = 32 s.
Q20. What is the least number which, when divided by 12, 6 and 8, leaves a remainder of 4 in each case?
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Answer: C. 28
LCM(12, 6, 8) = 24. Required number = 24 + 4 = 28.
Q21. What is the unit digit of 17^198?
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Answer: A. 9
Unit digits of 7^1, ^2, ^3, ^4 are 7, 9, 3, 1. 198 leaves remainder 2 on division by 4, so take the 2nd value in the cycle: 9.
Q22. If a + b = 7 and ab = 24, find a² + b².
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Answer: A. 1
a² + b² = (a + b)² − 2ab = 49 − 48 = 1.
Q23. Find the area of a circle of radius 21 cm. (Take π = 22/7)
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Answer: A. 1386 cm²
Area = 22/7 × 21 × 21 = 1386 cm².
Q24. In what ratio must rice at ₹40/kg be mixed with rice at ₹60/kg so that the mixture costs ₹48/kg?
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Answer: C. 3:2
Ratio = (60 − 48) : (48 − 40) = 12:8 = 3:2.
Q25. A invests ₹40000 for 12 months and B invests ₹35000 for 12 months. Out of a total profit of ₹10095, what is A's share (in ₹)?
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Answer: B. 5384
Ratio = 40000×12 : 35000×12 = 8:7. A's share = 10095 × 8/15 = ₹5384.