Work Problem - Ron Need your help

[sudhir.18n]

Source CAT- IIM India

An engineer undertakes a project to build a road 15 km long in 300 days and employs 45 men for the purpose. After 100 days, he finds only 2.5 km of the road has been completed. Find the (approximate) number of extra men he must employ to finish the work in time.
a. 43
b. 45
c. 55
d. 68
e. 60

OA is D
Can someone help me setup the RTD format for this particular question.

Ron Appreciate your help

[jnelson0612]

Hi sudhir,
I'm not Ron, but let me take a shot here. I'd use more of a logical reasoning strategy.

The workers were supposed to build a 15 km road in 300 days. After 100 days, they have only built 2.5 km. If you divide what they were supposed to get done by 3, you find that the 45 workers should have gotten 5 km built in 100 days. Thus, they are getting half as much done as they were supposed to.

Well, we still have 200 days left to work. Originally we were supposed to get 10 km built in these 200 days. If we double the crew of 45 we know that we can get this 10 km built on time, since twice as many workers can get twice as much done. So we need to add 45 workers and have 90 workers total. Thus, we know that the 90 workers can built 10 km in 200 days.

However, there's still the matter of the 2.5 km that we are behind at the end of the 100 days. We need to add some staff to make up for this shortcoming. Again, 90 workers can build 5 km in 100 days. For 2.5 km, that would be 45 workers. However, since we have 200 days in which to do the work, we only need half as many workers, or about 23.

Thus, we need 45 workers for kilometers 5 through 15, and 23 workers to make up the 2.5 km we are already short, or 68 total.

Hope this helps!

[sudhir.18n]

Hi Jamie ,
This how I approached the problem;

15 days*300 employees= 4500 Man hours =1/6th work( 2.5/15)
hence total work is 27000 man hours

(45+x)*200 = 5/6( remaining)* 27000
45+x= 22500/200
45+x = 113
x = 68

What do u think about this approach?
and at what level will you rate this question on GMAT ?

Thanks
Sudhir

[shoumik]

Nice solution Sudhir! Thanks!

[jnelson0612]

Hi Jamie ,
This how I approached the problem;

15 days*300 employees= 4500 Man hours =1/6th work( 2.5/15)
hence total work is 27000 man hours

(45+x)*200 = 5/6( remaining)* 27000
45+x= 22500/200
45+x = 113
x = 68

What do u think about this approach?
and at what level will you rate this question on GMAT ?

Thanks
Sudhir

Very nice work Sudhir! I think this is a 700-800 level problem.