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 alone.
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the time is taken more by 2 men and 7 boys
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Let,
- Time taken by 1 man = x days
- Time taken by 1 boy = y days
- work done by 2 men in 1 day = 2/x
- work done by 7 boys in 1 day = 7/y
Therefore,
2/x + 7/y = 1/4----------> [1]
Similarly ,
work done by 4 men in 1 day = 4/x
work done by 4 boys in 1 day = 4/y
4/x + 4/y = 1/3--------------> [2]
Multiplying equation [1] by 2
2(2/x + 7/y = 1/4 )
= 4/x + 14/y = 1/2------------> [3]
From equations [2] and [3]
y = 60
x = 15
∴ Time taken by 1 man to do the whole job = 15 days
∴ Time taken by 1 boy to do the whole job = 60 days
Together = 1/60 + 4/60 = 12 days
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