Quantitative Aptitude
Time and Work
2,195 Questions
Time and Work Questions
D
Correct answer
Explanation
Let M's rate be m, A's rate be 2m. Combined rate = 3m = 1/6. m = 1/18. Meenakshi takes 18 days.
B
Correct answer
Explanation
If A is twice as good as B, A's rate = 2B's rate. Together, their rate is 3B = 1/15 of the work per day. Thus, B's rate = 1/45, meaning B takes 45 days.
-
24 days
-
30 days
-
32 days
-
28 days
B
Correct answer
Explanation
Let B take x days, A takes x-10 days. Combined rate: 1/x + 1/(x-10) = 1/12. Solving x^2 - 34x + 120 = 0 gives (x-30)(x-4) = 0. Since x must be > 10, x = 30.
-
Rs. 1500
-
Rs. 2750
-
Rs. 2500
-
Rs. 2000
-
None of these
A
Correct answer
Explanation
Work rates: A = 1/15, B = 1/12. Together (A+B) = (4+5)/60 = 9/60 = 3/20. With boy (A+B+Boy) = 1/5 = 4/20. Boy's rate = 4/20 - 3/20 = 1/20. Ratio of work: A:B:Boy = 1/15 : 1/12 : 1/20 = 4:5:3. Total parts = 12. Boy's share = (3/12) * 6000 = 1500.
-
6 9/19 days
-
7 5/11 days
-
8 3/7 days
-
5 1/5 days
-
None of these
-
21 (1/7) days
-
26 (2/5) days
-
18 (6/17) days
-
23 (1/5) days
-
21 (3/5) days
-
7 5/13 days
-
9 4/7 days
-
6 3/22 days
-
8 6/17 days
-
None of these
C
Correct answer
Explanation
P rate = 1/18. Q rate = 1.2 * (1/18) = 1/15. Combined rate = 1/18 + 1/15 = (5+6)/90 = 11/90. Time for full work = 90/11. Time for 3/4 work = (3/4) * (90/11) = 270/44 = 135/22 = 6 3/22 days.
-
28 days
-
21 days
-
30 days
-
25 days
-
None of these
-
9 11/15 days
-
7 17/19 days
-
11 3/7 days
-
12 5/6 days
-
None of these
B
Correct answer
Explanation
Let M and W be the work done by one man and one woman per day. 10(7M + 9W) = 15(5M + 5W) => 70M + 90W = 75M + 75W => 5M = 15W => M = 3W. Total work = 10(7(3W) + 9W) = 10(30W) = 300W. 10M + 8W = 10(3W) + 8W = 38W. Time = 300W / 38W = 150/19 = 7 17/19 days.
-
24 days
-
28 days
-
32 days
-
20 days
-
None of these
B
Correct answer
Explanation
P, Q, R complete work in 20 days. Q and R complete 2/5 of work in 14 days, so they complete the whole work in 14 * 5/2 = 35 days. P's rate = 1/20 - 1/35 = (7-4)/140 = 3/140. P works for x days, so x * 3/140 = 3/5 (remaining work). x = (3/5) * (140/3) = 28.
-
10 men
-
9 men
-
8 men
-
6 men
-
None of these
C
Correct answer
Explanation
Total work is 20 men * 16 days = 320 man-days. After 5 days, 20 * 5 = 100 man-days are done, leaving 220 man-days. If x men remain, x * (55/3) = 220, so x = 12. Since 20 - 12 = 8 men left, the answer is 8.
-
8 days
-
10 days
-
5 ½ days
-
6 ¾ days
-
None of these
-
Rs. 850
-
Rs. 1000
-
Rs. 600
-
Rs. 700
-
None of these
B
Correct answer
Explanation
A's rate = 1/12, B's rate = 1/16. A+B+C rate = 1 / (16/3) = 3/16. C's rate = 3/16 - 1/12 - 1/16 = 2/16 - 1/12 = 1/8 - 1/12 = (3-2)/24 = 1/24. Share is proportional to work done. C's work = (1/24) / (3/16) = (1/24)*(16/3) = 2/9. Share = 4500 * 2/9 = 1000.
-
2 4/5 days
-
4 ½ days
-
3 ¾ days
-
5 1/3 days
-
None of these
A
Correct answer
Explanation
A does 1/10 work/day, B does 1/15 work/day. Let x be the days they worked together. (1/10 + 1/15) * x + (1/15) * 8 = 1. (3/30 + 2/30) * x + 8/15 = 1 => 5/30 * x = 7/15 => 1/6 * x = 7/15 => x = 42/15 = 14/5 = 2.8 days.
C
Correct answer
Explanation
Let A take x days, B+C take x+2 days. Together they take 60/11 days. (1/x) + 1/(x+2) = 11/60. Solving this: (2x+2)/(x^2+2x) = 11/60 -> 120x + 120 = 11x^2 + 22x -> 11x^2 - 98x - 120 = 0. Roots are x = 10.