7 men and 3 boys finish a job in 10 days, while 3 men and 7 boys finish it in 15 days. 10 boys working together will finish it in

A 40 days

B 16 days

C 42 days

D 25 days

E 24 days

Correct Answer: Option E

Let’s assume that one man can do the entire work alone in m days

And one boy can alone do the entire work alone in b days

∴part of work done by one man in one day = 1/m

and part of work done by one boy in one day = 1/b

Now, as per the given information:

Work was finished by 7 men and 3 boys in 10 days.

∴work done by 7 men and 3 boys in one day = 1/10

\(\Rightarrow 7 \times \frac{1}{m} + 3 \times \frac{1}{b} = \frac{1}{{10}}\) ------(i)

Also,

Work was finished by 3 men and 7 boys in 15 days.

∴work done by 3 men and 7 boys in one day = 1/15

\( \Rightarrow 3 \times \frac{1}{m} + 7 \times \frac{1}{b} = \frac{1}{{15}}\) ------(ii)

Solving equations (i) and (ii) simultaneously, we get:

(1/b) = (1/240)

∴part of work done by one boy in one day = 1/240

∵ since 10 boys are working together,

Part of work done by 10 boys in one day = 10/240 = 1/24

∴it will take 24 days for 10 boys to finish the entire work.