If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys c

Question

If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:

Options:

A . 4 days

B . 5 days

C . 6 days

D . 7 days

Answer: Option A

Let 1 man's 1 day's work = x and 1 boy's 1 day's work = y.

Then, 6x + 8y = \(\frac{1}{10}\) and 26x + 48y = \(\frac{1}{2}\) .

Solving these two equations, we get : x = \(\frac{1}{100}\) and y = \(\frac{1}{200}\) .

(15 men + 20 boy)'s 1 day's work = \(\left(\frac{15}{100}+\frac{20}{200}\right)=\frac{1}{4}.\)

so, 15 men and 20 boys can do the work in 4 days.

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