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?
Answers
The long it would take for one man and one boy to do it is :
• Let time taken by one man is x days and time taken by one boy is y days.
• Work done by one man in one day is 1/x and for boy is 1/y.
• Given : 2 men and 7 boys can do a piece of work in 4 days
°•° 2/x + 7/y = 1/4 ___ (1)
• Similarly, same work is done in 3 days by 4 men and 4 boys.
°•° 4/x + 4/y = 1/3
4×[ 1/x + 1/y ] = 1/3
1/x + 1/y = 1/12 ____(2)
Multiplying (2) by 2
2/x + 2/y = 1/6
• Subtracting (2) from (1)
( 2/x + 7/y ) - ( 2/x + 2/y ) = 1/4 - 1/6
7/y - 2/y = 1/12
12×( 7y - 2y ) = y^2
12×5y = y^2
y^2 = 60y
y = 60
• Substitute value of y in (2)
1/x + 1/60 = 1/12
1/x = 1/12 - 1/60
= 4 / 60
x = 60 / 4 = 15
• Time taken by one man is 60 days and time taken by one boy is 15 days.