Question

12 men and 16 boys can do a piece of work in 5 days; 13 men and 24 boys can do it in 4 days. The ratio of the daily work done by a man to that of a boy is

• A. 2 : 1
• B. 3 : 1
• C. 3 :2
• D. 5 : 4

Answer 1

The correct option is A 2 : 1

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

Then 12 x + 16y = $\frac{1}{5}.............\left(i\right)$

13x + 24y = $\frac{1}{4}.............\left(ii\right)$

Multiplying (i) by 3 and (ii) by 2 we get

36 x + 48y = $\frac{3}{5}.............\left(iii\right)$

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

Subtracting eqn (iv) from eqn (iii) we get $10x=\frac{3}{5}-\frac{1}{2}=\frac{6-5}{10}=\frac{1}{10}\Rightarrow x=\frac{1}{10}$

Putting x = $\frac{1}{100}$ in (i) we get $\frac{12}{100}+16y=\frac{1}{5}\Rightarrow 16y=\frac{1}{5}-\frac{12}{100}=\frac{20-12}{100}=\frac{8}{100}\Rightarrow y=\frac{1}{200}$

$\therefore$ Required ratio = $x:y=\frac{1}{100}:\frac{1}{200}=2:1$