General Aptitude › Time and Work › Question #4649
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QIf 2 men and 3 boys can complete a piece of work in 10 days, and 3 men and 2 boys can complete the same work in 8 days, how long will it take for 2 men and 1 boy to do the work ?

ID: #4649 Time and Work 221 views
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#4649Q ID
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Time and WorkTopic
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  • A 12.5 ✔ ✖
  • B 23.5 ✔ ✖
  • C 34.7 ✔ ✖
  • D 40.7 ✔ ✖
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Explanation

Let's suppose that the work done by 1 man in 1 day is x, and the work done by 1 boy in 1 day is y.

Then the work done by 2 men and 3 boys in 1 day is 2x + 3y, and the work done by 3 men and 2 boys in 1 day is 3x + 2y.

We are given that 2 men and 3 boys can complete the work in 10 days, so 2x + 3y = 1/10.

We are also given that 3 men and 2 boys can complete the work in 8 days, so 3x + 2y = 1/8.

Solving these equations for x and y, we get x = 7/200 and y = 1/100.

The work done by 2 men and 1 boy in 1 day is (2 * 7/200) + (1/100) = 16/200 = 2/25 of the total work.

Since 2 men and 1 boy complete (2/25) of the work in 1 day, it will take them 25/2 = 12 1/2 days to complete the entire work.
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