Quantitative Aptitude
Time and Work
2,195 Questions
Time and Work Questions
-
6 days
-
8 days
-
10 days
-
12 days
-
14 days
-
5 days
-
4 days
-
9 days
-
10 days
-
13 days
D
Correct answer
Explanation
16 men = 20 women, so 1 man = 1.25 women. 28 men + 15 women = 28(1.25) + 15 = 35 + 15 = 50 women. 20 women take 25 days, so 50 women take (20 * 25) / 50 = 10 days.
-
3 days
-
4 days
-
5 days
-
6 days
B
Correct answer
Explanation
Let M be men's work, W be women's work. 2(12M + 5W) = 5(4M + 3W) -> 24M + 10W = 20M + 15W -> 4M = 5W. 12M + 5W = 12M + 4M = 16M. Total work = 2 * 16M = 32M. 8 men take 32M / 8M = 4 days.
B
Correct answer
Explanation
A, B, and C work at rates of 1/12, 1/36, and 1/48 per day. In 2 days, they complete 2*(1/12 + 1/36 + 1/48) = 2*(12+4+3)/144 = 19/72. Then A and C work for 3 days, completing 3*(1/12 + 1/48) = 3*(5/48) = 15/48 = 5/16. The remaining work is 1 - (19/72 + 5/16) = 1 - (38+45)/144 = 1 - 83/144 = 61/144. C completes this at a rate of 1/48, taking (61/144) * 48 = 61/3 days.
C
Correct answer
Explanation
A does 1/5 in 10 days, so full job in 50 days. B does 1/3 in 25 days, so full job in 75 days. Combined rate = 1/50 + 1/75 = (3+2)/150 = 5/150 = 1/30. To do half the job, they need (1/2) / (1/30) = 15 days.
D
Correct answer
Explanation
Total work = 12 * 8 * 16 = 1536 man-hours. New requirement: 1536 / (8 * 12) = 16 men. Original men = 12. Additional men = 16 - 12 = 4.
D
Correct answer
Explanation
A's rate = 1/72, B's rate = 1/90. Combined rate = 1/72 + 1/90 = (5+4)/360 = 9/360 = 1/40. Work done in 10 days = 10 * (1/40) = 1/4. Work left = 1 - 1/4 = 3/4.
-
8 days
-
9 days
-
11 days
-
14 days
-
16 days
D
Correct answer
Explanation
B takes 20 days, A takes 30 days. Work rates: B=1/20, A=1/30. Together: 1/20+1/30 = 5/60 = 1/12. In 6 days, they do 6/12 = 1/2 work. Remaining 1/2. B does half of remaining (1/4) in 5 days. Remaining 1/4. A+B do 1/4 at rate 1/12 in 3 days. Total = 6+5+3 = 14 days.
B
Correct answer
Explanation
Work rate of A+B = 1/16. Work rate of A = 1/24. Work rate of B = 1/16 - 1/24 = (3-2)/48 = 1/48. B takes 48 days.
D
Correct answer
Explanation
A's rate is 1/15 and B's rate is 1/25. Let B work for x days. Then (1/15 + 1/25)x + (1/15)7 = 1. (8/75)x + 7/15 = 1. (8/75)x = 8/15. x = (8/15)(75/8) = 5 days.
B
Correct answer
Explanation
A's rate is 1/20, B's is 1/30. A works for 4 days, doing 4/20 = 1/5 of the work. Remaining work is 4/5. B and C complete this in 18 days, so (1/30 + C) * 18 = 4/5. Solving for C: 1/30 + C = 4/90 = 2/45. C = 2/45 - 1/30 = 4/90 - 3/90 = 1/90. Thus, C takes 90 days.
A
Correct answer
Explanation
A's work per day = 1/36. B's work per day = 1/12. Together = 1/36 + 3/36 = 4/36 = 1/9. In 3 days, they do 3 * (1/9) = 1/3. Work left = 1 - 1/3 = 2/3.
A
Correct answer
Explanation
Let boy efficiency = 1. Woman = 2, Man = 4. Total = 7 units/day. Total work = 7 * 7 = 49 units. Boy takes 49 / 1 = 49 days.
-
5 hours
-
10 hours
-
15 hours
-
18 hours
B
Correct answer
Explanation
Using the formula (M1*D1*H1) = (M2*D2*H2): 15 * 20 * 8 = 20 * 12 * H2. 2400 = 240 * H2, so H2 = 10.