Question

One man and 2 boys can do a work in 5 days. Two men and 1 boy can do the work in 4 days. In how many days can 1 man and 1 boy complete the work?​

Answer 1

Answer:

Let M be the proportion of the job that one man can complete in one day, and let B be the proportion of the job that one boy can complete in one day. We know:

1M + 2B = 1/5

2M + 1B = 1/4

Let's subtract twice the first equation from the second:

1M + 2B = 1/5

4M + 2B = 1/2

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-3M = -3/10

M = 1/10

So one man can do 1/10 of the job by himself per day.

1/10 + 2B = 1/5

2B = 1/10

B = 1/20

One boy can do 1/20 of the job by himself per day.

1 man + 1 boy can do 1/10 + 1/20 = 3/20 of the job in one day, so it would take them 20/3 (or 6 2/3) days.