swerve wrote:A contractor undertakes to dig a canal 12 km long in 350 days and employs 45 men. After 200 days he finds that only 4.5 km of canal has bee completed. Find the number of extra men he must employ to finish the work in time?

A. 53
B. 55
C. 43
D. 59
E. 48

The OA is B.

Please, can any expert explain this PS question for me? I can't get the correct answer. I need your help. Thanks.

For the purpose of this question lets use M instead of KM

Lets' work out the rate/speed per day of a man:

Men * Rate * Days = Work
45 * Rate * 200 = 4500
Rate = 0.5m/day

We have 7500m (12000 - 4500) to dig.

Let's work out how many men this would take in 150 days:
Men * Rate * Days = Work
Men * 0.5 * 150 = 7500
Men = 100

Extra men needed = 100 - 45 = 55

swerve wrote:A contractor undertakes to dig a canal 12 km long in 350 days and employs 45 men. After 200 days he finds that only 4.5 km of canal has bee completed. Find the number of extra men he must employ to finish the work in time?

A. 53
B. 55
C. 43
D. 59
E. 48

We can determine that the rate of the 45 men is 4.5/200 = 45/2,000 = 9/400.

We need to determine how many more men, working at the same constant rate must be used to dig another 7.5 km in 150 days. Thus, the entire crew needs to work at a rate of 7.5/150 = 75/1,500 = 1/20.

We can use a proportion to determine the total number of men needed to do the remainder of the job in the allotted time.

(x men)/(1/20) = (45 men)/(9/400)

9x/400 = 45/20

9x/400 = 9/4

9x/400 = 900/400

9x = 900

x = 100

Thus, the contractor needs to have a total crew of 100 men to complete the job on time. Since he already has 45 men, he needs to hire 100 - 45 = 55 more men.

Answer: B