Question

If 6 man and 8 boys can do a piece of work in 10 days, while 26 men and 48 boys can do the same work in 2 days, then what is the time taken by 15 men and 20 boys in doing the same type of work ?

• A. 3 days
• B. 4 days
• C. 5 days
• D. 6 days

Answer 1

The correct option is B 4 days

Let 1 man's 1 days' work = x and 1 boy's 1 days' work = y Then

$6x+8y=\frac{1}{10}..............\left(i\right)$

$26x+48y=\frac{1}{2}..............\left(ii\right)$

Performing (i) x 6 - (ii) we get

$(36x+48y)-(26x+48y)=\frac{6}{10}-\frac{1}{2}$ $\Rightarrow 10x=\frac{1}{10}\Rightarrow x=\frac{1}{100}$

Putting $x=\frac{1}{100}in\left(i\right)weget\frac{6}{100}+8y=\frac{1}{10}$

$\Rightarrow 8y=\frac{1}{10}-\frac{6}{100}=\frac{4}{100}\Rightarrow y=\frac{1}{200}$

$\therefore$ (15 men's+20 boys') 1 days' work = $=\frac{15}{100}+\frac{20}{200}=\frac{1}{4}$

$\therefore$ 15 men and 20 boys shall complete the work in 4 days