Question

4 men and 5 boys can do a piece of work in 20 days while 5 men and 4 boys can do the same work in 16 days. in how many days can 4 men and 3 boys do the same work?

Answer 1

Answer:

20 days

Step-by-step explanation:

4 men + 5 boys can complete a work in 20 days

Work completed by 4 men + 5 boys in 1 day=$\frac{1}{20}$---A

Work completed by 5 men + 4 boys in 1 day= $\frac{1}{16}$

Work done by 9 men + 9 boys in 1 day = $\frac{1}{20}+\frac{1}{16}=\frac{9}{80}$

So, work done by 1 man + 1 boy in 1 day=$\frac{1}{80}$

Work done by 4 men+ 4 boys in 1 day=$\frac{4}{80}=\frac{1}{20}$ ---B

Subtract B from A

Work done by 1 boy in 1 day =$\frac{1}{20}-\frac{1}{20}=0$

So, boy does no work.

Therefore work done by 4 men and 3 boys is same as work done by 4 men and 5 boys

Hence 4 men and 3 boys do the same work in 20 days.