Question

If $x$ men can do a piece of work in 5 days, then find the number of days that 20 men will take for the same work.

• A. $\frac{x}{6}days$
• B. $\frac{2x}{3}days$
• C. $\frac{x}{5}days$
• D. $\frac{x}{4}days$

Answer 1

The correct option is D $\frac{x}{4}days$

Given,
$x$ men can do a piece of work in 5 days.

We know that if the number of men increase, then the number of days taken to finish the piece of work will be less.

$\text{So, Number of men}\left(p\right)\propto \frac{1}{\text{Number of days}\left(q\right)}$
$\therefore \frac{p_1}{p_2}=\frac{q_2}{q_1}$

Given,
$p_1=xmen$
$p_2=20men$
$q_1=5days$
$\text{and}{q}_2=\text{No. of days taken by 20 men}$
$\Rightarrow \frac{x}{20}=\frac{q_2}{5}$
$\Rightarrow q_2=\frac{x\times 5}{20}$
$\Rightarrow d_2=\frac{x}{4}days$