Q. 214.1( 9 Votes )
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. How long would it take one man and one boy to do it?
To find: Time taken by one boy and 1 man.
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.
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
⇒ b = 60 days
Substitute the value of b in eq.2 to get,
⇒ a = 15 days
Thus 1 man can do work in 15 days and 1 boy can do work in 60 days.
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