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19 Feb 2024, 10:32
Kudos
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
70% (02:53) correct
30%
(03:00)
wrong
based on 144
sessions
History
Date
Time
Result
Not Attempted Yet
12 women can complete a project in 36 days and 15 men can complete the same project in 27 days. 16 women start working and after 6 days, they were replaced by x men. If x men complete the remaining work in 5 days then what is the value of x?
A. 40
B. 42
C. 45
D. 57
E. 63
A. 40
B. 42
C. 45
D. 57
E. 63
19 Feb 2024, 10:52
Kudos
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Shubhradeep
The amount of the work = 12 women * 36 = 15 men * 27
- 12w*36 = 15m*27
16w = 15m
The project was done by 16 women working for 6 days and by x men working for 5 days. Hence, the amount of the work also equals to 16w*6 + 5mx. Equating this to 15m*27 gives:
- 16w*6 + 5mx = 15m*27.
Since 16w = 15m, then we'd get:
- 15m*6 + 5m*x = 15m*27
Reducing by m yields:
- 15*6 + 5x = 15*27
x = 63.
Answer: E.
19 Feb 2024, 10:55
Kudos
Bookmarks
Shubhradeep
12 women can complete a project in 36 days
So, 12 women in 6 days complete 6/36 = 1/6 th of the work
So, 1 woman in 6 days complete 1/(6*12) th of the work
So, 16 women in 6 days complete 16/(6*12) = 2/9 th of the work
Remaining work = 7/9 th part
We know that 15 men do the work in 27 days
So, to do the work in 1 day, we would need 15 * 27 men
So, to do the work in 5 days, we would need 15 * 27/5 = 81 men
So, to do 7/9 th of the work in 5 days, we would need 81 * 7/9 = 63 men
Thus, x = 63
Alt: Work of 12 women in 36 days = work of 15 men in 27 days
If efficiency of a woman = 1 unit of work per day, we have:
Total work = 12 * 36 units = 432 units
Also Work of 15 men in 27 days = 12 * 36 units
=> Efficiency of a man = 12*36/(15*27) = 16/15 unit per day
Work done by 16 women in 6 days = 16*6 = 96 units
Work remaining = 432 - 96 = 336 = Work done by x men in 5 days
=> 336 = x * 16/15 * 5
=> x = 63
