Four men and 6 women can complete a certain piece of work in 5 days whereas three men and 4 women can complete it in 7 days. How many men should assist 25 women to complete $2\frac{1}{2}$ times the same work in 5 days?
Answer & explanation
Correct answer: option 4
4M + 6W = 5 days,
20M + 30W ..(1) (Multiplied by 5 to get it done in 1 day)
3M + 4W = 7 days,
21M + 28W ..(2) (Multiplied by 15 to get it done in 1 day)
Now, (1) - (2), we get
⇒ M = 2W
⇒ M : W = 2 : 1 (Efficiencies)
Putting efficiency in equation (2), and we get the total work
⇒ [21 (2) + 28 (1)] = 70 units.
⇒ \( {2 }_{ 2}^{ 1} \) of 70 = 175 units.
⇒ No. of men needed to assist 25W to complete 175 units in 5 days = \(\frac{175}{25+2M}\) ..
⇒ M = 5 men.
Therefore 5 men are needed to assist 25 women to complete 175 units of work in 5 days.