. 2 men and 3 women finish 25% of the work in 4 days, while 6 men and 14 women can finish the whole work in 5 days. in how many days will 20 women finish it?
Answers
20 women will finish the whole work in 20 days.
Step-by-step explanation:
Let men be denoted as “M” and women be denoted as “W”.
According to the data in the question and using the Man-Days formula, we get
[(2M+3W) * 4] / [25/100] = [(6M+14W) * 5] / [1]
⇒ [(2M+3W) * 4] / [1/4] = [(6M+14W) * 5]
⇒ [(2M+3W) * 4 * 4] = [(6M+14W) * 5]
⇒ 32M + 48W = 30M + 70W
⇒ 32M - 30M = 70W - 48W
⇒ 2 M = 22W
⇒ M = 11W ....... (i)
Now, substituting from (i), we have
6M + 14W = 6*(11W) + 14W = 66W + 14W = 80W ← will finish the work in 5 days.
Let 20 women finish the whole work in "D" days.
Therefore, by again using the Man-days formula, we get
80 W * 5 = 20W * D
⇒ D = 4 * 5
⇒ D = 20 days
Thus, in 20 days, 20 women will finish the whole work.
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