8 men and 10 women are working together on a job and can complete it in 10 days. The work done by each woman is four-fifth of the work by each man. In how many days 10 men alone can complete the same work?
1) 20 days
(2) 12 days
(3) 15 days
(4) 16 days
Answers
10 men alone can complete the whole work in option (4): 16 days.
Step-by-step explanation:
Let men be denoted as “M” and women be denoted as “W”.
It is given that,
8M + 10W can complete the job in 10 days
Work done by 1 women = 4/5th of work done by 1 men
i.e., 1W = 4/5 * 1M
⇒ W = 4M/5 ……. (i)
Therefore, substituting from (i), we get
8M + 10W = 8M + (10*4/5 *M) = 8M + 8M = 16M ← can complete the job in 10 days
Let the no. of days 10 men would alone require to complete the job be denoted as “D” days.
Using the Man-Days formula, we get
16M * 10 = 10M * D
⇒ D = [16 * 10] / 10
⇒ D = 16 days
Thus, in 16 days, 10 men can alone complete the same work.
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