Q1. A and B together can finish a job in 16 days. A alone can finish it in 24 days. How many days will B alone take?
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Answer: B. 48 days
B's work per day = 1/16 − 1/24 = 1/48. So B alone takes 48 days.
SSC CGL Quantitative Aptitude Intermediate Practice Set 4
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, Geometry, Mixture and Alligation, Partnership, Simplification, Percentage, Discount, Simple Interest, Average, Ratio and Proportion, Mensuration
Score: 0 / 0
Q2. A train 400 m long runs at 45 km/h. How long will it take to cross a platform 325 m long?
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Answer: A. 58 seconds
Speed = 45 × 5/18 = 12.5 m/s. Distance = 400 + 325 = 725 m. Time = 725/12.5 = 58 s.
Q3. What is the least number which, when divided by 18, 15 and 16, leaves a remainder of 2 in each case?
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Answer: D. 722
LCM(18, 15, 16) = 720. Required number = 720 + 2 = 722.
Q4. What is the unit digit of 3^90?
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Answer: A. 9
Unit digits of 3^1, ^2, ^3, ^4 are 3, 9, 7, 1. 90 leaves remainder 2 on division by 4, so take the 2nd value in the cycle: 9.
Q5. If a + b = 14 and ab = 19, find a² + b².
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Answer: C. 158
a² + b² = (a + b)² − 2ab = 196 − 38 = 158.
Q6. A father's age is 3 times his son's age. After 11 years, the father will be 2 times as old as his son. What is the son's present age?
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Answer: A. 11 years
3x + 11 = 2x + 22 ⇒ x = 11 ⇒ x = 11 years.
Q7. What is the measure of each interior angle of a regular polygon with 15 sides?
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Answer: D. 156°
(15 − 2) × 180/15 = 156°.
Q8. In what ratio must rice at ₹30/kg be mixed with rice at ₹50/kg so that the mixture costs ₹40/kg?
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Answer: A. 1:1
Ratio = (50 − 40) : (40 − 30) = 10:10 = 1:1.
Q9. A invests ₹50000 for 12 months and B invests ₹35000 for 12 months. Out of a total profit of ₹24446, what is A's share (in ₹)?
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Answer: D. 14380
Ratio = 50000×12 : 35000×12 = 10:7. A's share = 24446 × 10/17 = ₹14380.
Q10. Find the value of √1521 + 2².
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Answer: D. 43
√1521 = 39; 2² = 4; total = 43.
Q11. The price of an item rises from ₹700 to ₹1050. What is the percentage increase?
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Answer: A. 50%
Increase = 1050 − 700 = 350. % increase = 350/700 × 100 = 50%.
Q12. The marked price of a shirt is ₹6500. A discount of 25% is given. What is the selling price (in ₹)?
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Answer: A. 4875
SP = 6500 × 75/100 = ₹4875.
Q13. A sum of ₹3500 amounts to ₹3780 in 2 years at simple interest. What is the rate of interest per annum?
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Answer: A. 4%
SI = 3780 − 3500 = ₹280. R = 280 × 100 / (3500 × 2) = 4%.
Q14. The average age of 40 students in a class is 26 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: D. 67 years
Teacher's age = (40 + 1) × 27 − 40 × 26 = 1107 − 1040 = 67 years.
Q15. If A:B = 7:3 and B:C = 5:2, find A:B:C.
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Answer: D. 35:15:6
Multiply the first ratio by 5 and the second by 3: A:B:C = 35:15:6 = 35:15:6.
Q16. A and B together can finish a job in 20 days. A alone can finish it in 36 days. How many days will B alone take?
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Answer: B. 45 days
B's work per day = 1/20 − 1/36 = 1/45. So B alone takes 45 days.
Q17. A train 100 m long runs at 72 km/h. How long will it take to cross a platform 300 m long?
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Answer: C. 20 seconds
Speed = 72 × 5/18 = 20 m/s. Distance = 100 + 300 = 400 m. Time = 400/20 = 20 s.
Q18. What is the least number which, when divided by 30, 18 and 6, leaves a remainder of 4 in each case?
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Answer: C. 94
LCM(30, 18, 6) = 90. Required number = 90 + 4 = 94.
Q19. What is the unit digit of 3^75?
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Answer: B. 7
Unit digits of 3^1, ^2, ^3, ^4 are 3, 9, 7, 1. 75 leaves remainder 3 on division by 4, so take the 3rd value in the cycle: 7.
Q20. If a + b = 13 and ab = 25, find a² + b².
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Answer: A. 119
a² + b² = (a + b)² − 2ab = 169 − 50 = 119.
Q21. A father's age is 4 times his son's age. After 10 years, the father will be 3 times as old as his son. What is the son's present age?
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Answer: B. 20 years
4x + 10 = 3x + 30 ⇒ x = 20 ⇒ x = 20 years.
Q22. Find the circumference of a circle of radius 7 cm. (Take π = 22/7)
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Answer: C. 44 cm
C = 2 × 22/7 × 7 = 44 cm.
Q23. What is the measure of each interior angle of a regular polygon with 9 sides?
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Answer: D. 140°
(9 − 2) × 180/9 = 140°.
Q24. In what ratio must rice at ₹10/kg be mixed with rice at ₹20/kg so that the mixture costs ₹13/kg?
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Answer: B. 7:3
Ratio = (20 − 13) : (13 − 10) = 7:3.
Q25. A invests ₹50000 for 12 months and B invests ₹35000 for 8 months. Out of a total profit of ₹10956, what is A's share (in ₹)?
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Answer: B. 7470
Ratio = 50000×12 : 35000×8 = 15:7. A's share = 10956 × 15/22 = ₹7470.