Question

If $10$ men, working $7$ hours a day dig a trench $147$ m long, how many men working $8$ hours a day will dig a trench $168$ m long (of the same breadth and depth as the first in the same number of days)?

Answer 1

No. of men required to complete a work $\propto$ Work Done

No. of men required to complete a work $\propto \frac{1}{\text{Time taken in hours}}$

Work Done $\propto$ Time taken in hours

Therefore, $\frac{M_1{H}_1}{W_1}=\frac{M_2{H}_2}{W_2}$

where,
$M$ is the no. of men,
$H$ is no. of hours and
$W$ is the work done

From the given information:
$M_1=10,H_1=7,W_1=147,M_2=?,H_2=8$ and $W_2=168$

Putting the values in the given formula, we get,

$\Rightarrow \frac{10\times 7}{147}=\frac{M_2\times 8}{168}$

$\Rightarrow M_2=\frac{10\times 7\times 168}{147\times 8}=10$

Thus, $10$ men are required to complete the given work in given time.