A contractor employs 45 men to dig a canal, 12 km long, in 350 days. After 200 days, he finds that only 4.5 km of the canal has been completed. Find the number of extra men he must employ in order to complete the work on time.

Correct option is A

Given:

45 men dig 12 km in 350 days.

4.5 km completed in 200 days. 

Solution:
Remaining work:

​$$12 - 4.5 = 7.5 \, \text{km in} \, 150 \, \text{days.}$$​​

Work rate per day:

​$$\text{Rate} = \frac{12}{350} = \frac{6}{175} \, \text{km per day by 45 men.}$$​​

Remaining rate required:

​$$\frac{7.5}{150} = 0.05 \, \text{km/day.}$$​​

Number of men needed:

​$$\frac{0.05}{\frac{6}{175}} \times 45 = 100 \, \text{men.}$$​​

Extra men:

100 − 45 = 55 

Alternate Method:  

12 - 4.5 = 7.5 km in, 150 days.

M₁ = 45 , M₂ =?

W₁ = 4.5 ,W₂ = 7.5

D₁= 200 , D₂ = 150

$$\frac{M_1 \times D_1}{W_1} = \frac{M_2 \times D_2}{W_2} \\ \ \\ \frac{45 \times200}{4.5} = \frac{M_2 \times 150}{7.5} \\ \ \\ M_2 = 100 \ men$$  

Extra men = 100 - 45 = 55