Question

2 men and 7 boys can do a piece of work in 14 days, 3 men and 8 boys can do the same work In 11 days. 8 men and 6 boys can do 3 times the amount of this work in ______.

• A. $21$ days
• B. $18$ days
• C. $24$ days
• D. $36$ days

Answer 1

The correct option is A $21$ days

This question can be solved in two steps:

1. Equate the work done by both groups in one day to find out the relation between work done by man and boy.
2. Once we have the relation from step 1 , use that to convert everything into one group to make the comparison easy.

2 men and 7 boys are required to complete the work in 14 days. So 28 men $(2\times 14)$ and 98 boys $(7\times 14)$ are required to complete the work in one day. 3 men and 8 boys are required to complete the work in 11 days. So 33 men $(3\times 11)$ and 88 boys $(8\times 11)$ are required to complete the work in one day. Now, equate the two cases as $28m+98b=33m+88b⟹1m=2b⟹1men=2boys$ . So now we can convert both the groups into one group (group of men or group of boys)

Converting both the groups as group of only men:

3 men and 8 boys= 3 men and 4 men = 7 men . So 7 men can finish the work in 11 days$⟹$ 11 men can finish the work in 7 days.

8 men and 6 boys= 8 men and 3 men = 11 men . So 11 men can finish the work in 7 days.

To complete the work of 3 times the actual work, $7\times 3=21days$ are required