Quantitative Aptitude
Time and Work
2,195 Questions
Time and Work Questions
D
Correct answer
Explanation
If A is twice as good as B, A's rate is 2B. Combined rate is 3B. 3B * 14 = 1 (total work). B = 1/42. A = 2B = 2/42 = 1/21. A takes 21 days.
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$\displaystyle\frac{x}{100y(1-z)}$days
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$\displaystyle\frac{100yz}{x}$days
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$\displaystyle\frac{100x}{y(100-z)}$days
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$\displaystyle\frac{100}{y(z-1)}$days
C
Correct answer
Explanation
The company produces y goods daily, but z% are unfit, so effective production is y * (1 - z/100) = y * (100 - z) / 100. To produce x goods, the time required is x / (effective production) = x / (y * (100 - z) / 100) = 100x / (y * (100 - z)).
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$\displaystyle 13\frac{1}{2}$
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$\displaystyle 4\frac{1}{2}$
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$6$
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$3$
C
Correct answer
Explanation
P's rate = 1/9 work/day. Q is 50% more efficient, so Q's rate = 1.5 * (1/9) = 3/2 * 1/9 = 1/6 work/day. Time taken by Q = 1 / (1/6) = 6 days.
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$\displaystyle 13\frac{1}{3}$ days
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$15$ days
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$20$ days
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$30$ days
A
Correct answer
Explanation
A = 0.5B. C = 0.5(A+B) = 0.5(1.5B) = 0.75B. C does work in 40 days, so total work = 40 * 0.75B = 30B. A+B+C = 0.5B + B + 0.75B = 2.25B. Time = 30B / 2.25B = 30 / 2.25 = 13.33 days.
C
Correct answer
Explanation
A's rate = (3/4)/18 = 1/24 per day. B's rate = (2/3)/12 = 1/18 per day. C's rate = 0.6/24 = 1/40 per day. Work done = 4*(1/24) + 6*(1/18) + 8*(1/40) = 1/6 + 1/3 + 1/5 = (5+10+6)/30 = 21/30 = 0.7. Pending work = 1 - 0.7 = 0.3 or 30%.
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$2$ days
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$3$ days
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$4$ days
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$5$ days
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None of these
A
Correct answer
Explanation
Total work = 12 * 9 = 108 man-days. Work done in 6 days = 12 * 6 = 72 man-days. Remaining work = 108 - 72 = 36 man-days. With 12+6 = 18 men, time = 36/18 = 2 days.
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$5$
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$6$
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$7\dfrac {1}{2}$
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$7$
B
Correct answer
Explanation
5/8 of job in 10 days. 1/8 of job in 2 days. Remaining 3/8 of job in 3 * 2 = 6 days.
D
Correct answer
Explanation
Let x be the original number of workers. The total work is 25x. After 6 workers leave, the remaining (x-6) workers finish in 40 days, so 40(x-6) = 25x. Solving 40x - 240 = 25x gives 15x = 240, so x = 16.
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${ 7 }_{ 4 }^{ 3 }$
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${ 8 }_{ 5 }^{ 4 }$
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${ 9 }_{ 8 }^{ 3 }$
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10 days
C
Correct answer
Explanation
A does 1/3 in 5 days, so A takes 15 days for the whole work. B does 2/5 in 10 days, so B takes 25 days for the whole work. Combined rate = 1/15 + 1/25 = (5+3)/75 = 8/75. Time = 75/8 = 9 and 3/8 days.
B
Correct answer
Explanation
Rates: P=1/10, Q=1/12, R=1/15. Combined rate = (6+5+4)/60 = 15/60 = 1/4. Time = 4 days.
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8 days
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9 days
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10 days
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none
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$12$
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$27$
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$10$
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$\dfrac{16}{3}$
B
Correct answer
Explanation
Using M1D1 = M2D2: 12 * 18 = 8 * D2. D2 = (12 * 18) / 8 = 216 / 8 = 27.
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$30$ days
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$40$ days
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$45$ days
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$50$ days
B
Correct answer
Explanation
Rates: A+B=1/15, B+C=1/20, A+C=1/30. Summing: 2(A+B+C) = 1/15 + 1/20 + 1/30 = (4+3+2)/60 = 9/60 = 3/20. So A+B+C = 3/40. A = (A+B+C) - (B+C) = 3/40 - 1/20 = 1/40. A takes 40 days.
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$15$ days
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$14$ days
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$13$ days
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$10$ days
A
Correct answer
Explanation
A does 5/40 = 1/8 of the work. Remaining work = 7/8. B does 7/8 in 21 days, so B's rate is (7/8) / 21 = 1/24. Together, their rate is 1/40 + 1/24 = (3+5)/120 = 8/120 = 1/15. They take 15 days together.