Question

12 men can do a work in 9 days. If 6 more men are engaged to do the same work, then how long will it take to complete the same work?

• A. 8 days
• B. 6 days
• C. 4 days
• D. 5 days

Answer 1

The correct option is B 6 days

Given,
12 men can complete a work in 9 days.

We know that more the number of men, the lesser will be the time taken to complete the work.

$So,\text{Number of men}\left(x\right)\propto \frac{1}{\text{Time}\left(y\right)}$
$\therefore \frac{x_1}{x_2}=\frac{y_2}{y_1}$

Given,
$x_1=12\text{men}$
$y_1=9\text{days}$
$x_2=(12+6)=18\text{men}$
$\text{and}{y}_2=\text{number of days}$

$\Rightarrow y_2=\frac{x_1\times y_1}{x_2}$
$\Rightarrow y_2=\frac{12\times 9}{18}=6\text{days}$