2 men and 7 boys can …

Let the time in which man can finish the work in x days and the boy can finish the same work in y days.

Total work done = work done in one day {tex}\times{/tex} number of days

Work done by one man in one day = {tex}\frac { 1 } { x }{/tex}

and work done by one boy in one day ={tex}\frac { 1 } { y }{/tex}

{tex}\frac { 2 } { x } + \frac { 7 } { y } = \frac { 1 } { 4 }{/tex} ....(i)

{tex}\frac { 4 } { x } + \frac { 4 } { y } = \frac { 1 } { 3 }{/tex} ....(ii)

Let {tex}\frac { 1 } { x }{/tex} be a and {tex}\frac { 1 } { y }{/tex} be b , then 

{tex}2 a + 7 b = \frac { 1 } { 4 }{/tex} ....(iii)

{tex}4 a + 4 b = \frac { 1 } { 3 }{/tex} ....(iv)

On Multiplying eqn. (iii) by 2 and subtract eqn. (iv)
from it

we get, {tex}b = \frac { 1 } { 60 }{/tex}

Put {tex}b = \frac { 1 } { 60 }{/tex} in equation (iii),

{tex}2 a + \frac { 7 } { 60 } = \frac { 1 } { 4 }{/tex}

{tex}\Rightarrow \quad 2 a = \frac { 1 } { 4 } - \frac { 7 } { 60 }{/tex}

{tex}\Rightarrow \quad a = \frac { 1 } { 15 }{/tex}

So, {tex}\frac { 1 } { 15 } = \frac { 1 } { x }{/tex}

{tex}\therefore {/tex}{tex}x=15{/tex} 

Also, {tex}b = \frac { 1 } { 60 }=\frac { 1} { y }{/tex}

Hence, y = 60

Therefore , the man can finish the work alone in 15 days and the boy in 60 days.