Let the number of days in which 1 man and 1 boy can do the work be ‘a’ and ‘b’ respectively.

In 1 day, 1 man does 1/a part and 1 boy does 1/b part.

Given, 2 men and 7 boys can do a piece of work in 4 days. The same work is done in 3 days by 4 men and 4 boys.

-------- (1)

-------- (2)

Multiplying eq1 by 2 and subtracting eq2 from eq1

⇒ 10/b = 1/6

⇒ b = 60 days

Thus, 4/a + 1/15 = 1/3

⇒ 4/a = 4/15

⇒ a = 15 days