Question

175 men can dig a canal 3150 m long in 36 days. How many men are required to dig a canal 3900 m long in 24 days?

• A. 256
• B. 225
• C. 325
• D. 384

Answer 1

The correct option is C

325

$\begin{array}{ccc}\text{No.of men}& \text{Length}& \text{No.of days}\\ 175& 3150& 36\\ X& 3900& 24\end{array}$

We'll define a new variable
$\text{Number of man days (N)}$

$N=\text{No. of men}\times \text{No of days}$

$N_1=175\times 36=6300$

$N_2=X\times 24=24X$

Let length of the canal dug be $L$

Number of man days is directly proportional to the length of the canal dug.

$\frac{N_1}{N_2}=\frac{L_1}{L_2}$

$\Rightarrow \frac{6300}{24X}=\frac{3150}{3900}$

$\Rightarrow X=\frac{3900}{12}=325$

Hence, 325 men are required to dig a length of 3900m in 24 days.