A contractor undertakes to dig a canal 12km long in 350 days and employs 45 men.After 200 days he finds that only 4.5km of canal has been 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


Source: quicker maths

A contractor undertakes to dig a canal 12km long in 350 days and employs 45 men.After 200 days he finds that only 4.5km of canal has been 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

let x=km per man per day
45*x*200=4.5 km
x=1/2000 km
let y=additional men needed
(45+y)*1/2000*150=7.5 km
y=55
B

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 men need 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 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
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