Quantitative Aptitude
Time and Work
2,195 Questions
Time and Work Questions
C
Correct answer
Explanation
Work = 2 persons * 3 days = 6 man-days. If only 1 person works, time = 6 man-days / 1 person = 6 days.
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$12$ days
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$20$ days
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$25$ days
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$28$ days
B
Correct answer
Explanation
The combined rate of A and B is 1/(20/3) = 3/20 work per day. Since B's rate is 1/10 work per day, A's rate is 3/20 - 1/10 = 3/20 - 2/20 = 1/20 work per day. Thus, A takes 20 days to complete the work alone.
B
Correct answer
Explanation
Let x be the total days. A works for x days, B works for x-4 days. (x/10) + ((x-4)/20) = 1. Multiplying by 20 gives 2x + x - 4 = 20, so 3x = 24, x = 8.
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$3$ days
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$4$ days
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$4.5$ days
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None
A
Correct answer
Explanation
A's total work time = 7 * 9 = 63 hours. B's total work time = 6 * 7 = 42 hours. Combined rate = 1/63 + 1/42 = (2+3)/126 = 5/126 work per hour. Working 42/5 hours a day, daily work = (5/126) * (42/5) = 1/3 of the work per day. Total days = 3.
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$\cfrac{1}{4}$
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$\cfrac{1}{10}$
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$\cfrac{7}{15}$
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$\cfrac{8}{15}$
D
Correct answer
Explanation
A's rate = 1/15, B's rate = 1/20. Combined rate = 1/15 + 1/20 = 7/60. Work done in 4 days = 4 * (7/60) = 7/15. Work left = 1 - 7/15 = 8/15.
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$12$ days
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$13$ days
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$13\dfrac{2}{7}$ days
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None of these
D
Correct answer
Explanation
A's rate is 1/16, B's is 1/12. In 2 days, they complete 1/16 + 1/12 = 7/48. In 12 days (6 cycles), they complete 6 * (7/48) = 42/48 = 7/8. Remaining work is 1/8. On day 13, A works and completes 1/16. Remaining is 1/8 - 1/16 = 1/16. On day 14, B completes it in (1/16) / (1/12) = 3/4 days. Total time = 13.75 days.
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$8$ days
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$12$ days
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$13$ days
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$15$ days
D
Correct answer
Explanation
Let Kewal take x days. Harpal takes x/3 days. Given x - x/3 = 10, so 2x/3 = 10, which means x = 15.
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Man: $160$ days. Boy : $190$ days
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Man: $140$ days. Boy : $280$ days
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Man: $240$ days. Boy : $150 $days
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Man: $260$ days. Boy : $200$ days
B
Correct answer
Explanation
Let M be man's rate, B be boy's rate. 8M + 12B = 1/10; 6M + 8B = 1/14. Solving this system: 24M + 36B = 3/10; 24M + 32B = 4/14 = 2/7. Subtracting: 4B = 3/10 - 2/7 = (21-20)/70 = 1/70. B = 1/280. 6M + 8(1/280) = 1/14 => 6M + 1/35 = 1/14 => 6M = 5/70 - 2/70 = 3/70. M = 1/140. Times are 140 and 280.
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$5$ days
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$\dfrac{11}{2}$ days
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$6$ days
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$8$ days
C
Correct answer
Explanation
A's rate is 1/18 work/day and B's rate is 1/15 work/day. B worked for 10 days, completing 10/15 = 2/3 of the work. The remaining 1/3 of the work is completed by A in (1/3) / (1/18) = 6 days.
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$6$ days
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$7.5$ days
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$8 $ days
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$8.5$ days
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$4$ days
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$5$ days
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$9 $ days
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$10$ days
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$18$ days
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$15$ days
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$12$ days
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$\displaystyle 7\frac{1}{2}$ days
A
Correct answer
Explanation
A+B rate = 1/6. A rate = 1/9. B rate = 1/6 - 1/9 = 3/18 - 2/18 = 1/18. B takes 18 days.
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$60$ days
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$\displaystyle 10\frac{15}{36}$days
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$40$ days
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$50$ days
A
Correct answer
Explanation
This is an inverse proportion problem. 36 men * 25 days = 15 men * x days. x = (36 * 25) / 15 = 36 * (5/3) = 12 * 5 = 60 days.
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$4\displaystyle\frac{4}{9}$ days
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$5\displaystyle\frac{3}{9}$ days
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$5\displaystyle\frac{1}{2}$ days
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$4\displaystyle\frac{7}{9}$ days
A
Correct answer
Explanation
Work done by me in 1 day = 1/8. Work done by you in 1 day = 1/10. Together = 1/8 + 1/10 = (5+4)/40 = 9/40. Time = 40/9 = 4 4/9 days.
C
Correct answer
Explanation
If A takes 9 days, A's efficiency is 1/9 of the work per day. B is 50% more efficient than A, meaning B's efficiency is 1.5 times A's, which is 1.5 * (1/9) = 1/6. Thus, B takes 6 days to complete the work.