Question : 3 men and 7 women can do a job in 5 days, while 4 men and 6 women can do it in 4 days. The number of days required for a group of 10 women working together, at the same rate as before, to finish the same job is:
Option 1: 30 days
Option 2: 36 days
Option 3: 40 days
Option 4: 20 days
Correct Answer: 20 days
Solution :
Given: 3 men and 7 women can do a job in 5 days, while 4 men and 6 women can do it in 4 days.
We know the formula, $M_1\times D_1 =M_2\times D_2$.
According to the question,
3 × 5 men + 7 × 5 women = 4 × 4 men + 6 × 4 women
(16 – 15) men = (35 – 24) women
1 man = 11 women
Also, 3 men + 7 women = 3 × 11 women + 7 women.
= 40 women
Again use, $M_1\times D_1 =M_2\times D_2$.
⇒ 40 × 5 = 10 × $D_2$
$D_2= 20$ days
Hence, the correct answer is 20 days.
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