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.
To find:
How long would it take one man and one boy to do it.
Solution:
Let the number of days in which 1 man and 1 boy can do the work be ‘a’ and ‘b’ respectively.
In 1 day,In a days 1 man can work
⇒ In 1 day 1/a man can do work
⇒ 2 men can do work in 2/a days
Similarly
In b days 1 boy can work
⇒ In 1 day 1/b boy can do work
⇒ 7 boys can do work in 7/b days
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.
Multiplying eq1 by 2 and subtracting eq2 from eq1
⇒ 10/b = 1/6
⇒ b = 60 days
Substitute the value of b in eq.2
Thus,
4/a + 1/15 = 1/3
⇒ 4/a = 4/15
⇒ a = 15 days
Thus 1 man can do work in 15 days and 1 boy can do work in 60 days.
