An engineer undertakes a project to build a road 15 km long in 300 day

45 workers working already

Let x be the total men required to finish the task in next 200 days

2.5 km done hence remaining is 12.5 km
Also, work has to be completed in next 200 days (300 - 100 = 200)

We know that, proportion of men to distance is direct proportion
and, proportion of men to days is inverse proportion

Hence, X = (45 * 12.5 * 100) / (2.5 * 200)
thus, X = 112.5 that is approximately 113

Thus, more men needed to finish the task = 113-45=68
hence Answer is D

Can someone set up the RTD/RTW format of manhattan gmat for me . Finding it difficult to put it in that format
Thanks
I know it in the typical CAT format;

total man hours = 4500 = 16.66%
hence 83.33% = 22500
thus total employees = 22500/200 = 113 ,which is 68 more than 45

the ratios are :
1. work 2.5 : 12.5 direct proportion to the number of men increasing.
2 time 200:100 inverse proportion to the men increasing
3 men 45 : x increasing number of men.

thus, 12.5 * 100*45/ 2.5 * 200 = 112.5
difference 112.5-45 = 68 approx.

Hence D.

45 M - 100 Days - 2.5 Km


45 M - 40 Days - 1 Km of road

45 * 40 Man days - 1 km of road

12.5 km = 12.5 * 1800 Man days


# of men = 12.5 * 1800/200 = 12.5 * 9 = 112.5

Extra men = 112.5 - 45 = 67.5 ~ 68

Answer - D

in 100 days 45 men have completed 2/12 of job
to complete entire job in 300 days 45+m men must complete 5/12 of job in each of the next two 100 day periods
(45+m)/45=5/2
m=67.5➡68 men

let r=rate=meters of road one man can complete in one day
r=2500 meters/4500 man days=5/9 meter per day
let m=number of extra men needed to complete work on time
(200 days)(45+m men)(5/9 meter per day)=12,500 meters
m=67.5➡68 men

We can use the formula
P1XT1/W1=P2XT2/W2
were
P=no of people/machines etc
T=days/time/mins etc
W=work to be done
Putting the respective values
45menx100days/2.5kms=M2x200days/12.5kms
Solving the equation M2 =112.5. Rounding off to 113. Men already working 45 hence extra men required 113-45=68

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I probably took the the longer method - But got the right answer ->

45 men completed 2.5kms in 100 days
work remaining = 12.5 km, days remaining = 200

=> 45 men will complete 5kms in 200 days (from 2.5kms in 100 days)
5 kms - 45 men
12.5kms - 45 *12.5/5 = 112.5 men (approx 113 men needed)
No. of more men needed to finish the task = 113 - 45 = 68

Is this approach correct.?

In above question, it is mentioned that the employees has completed 2.5 km only by 100 days.
as per this rate the will accomplish this job......
ATQ, 2.5km is completed in 100 days
1 km is completed in 100/2.5 days
15 km is completed in {(100/2.5)*15} or 600 days
it means the under taken project deadline will transcend the deadline by 300 days, by all means 600 days total.
In this case, let the engineer must employ X people to pursue the estimated deadline.
He can peruse this job using a simple calculation.....
......As per this current rate he needs 600 days
......100 days have been passed doing partial amount of work
......we need to reduce 300 days employing X people to meet deadline
...... so we have 200 days in our hand
then,
200= {45*(600-100}/(45+X)}
> X = {(45*500)/200} -45
> X = 67.5 people(Apprx..)= 68 people
_________________
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regards,
Jamil_Mehedi

Seems correct to me.

Total Mandays for \(2.5 Km = 4500\)
Total Mandays for \(12.5 Km = x\)
\(x = 22,500\)
\(Number of men * Days = 22,500\)
\(Days = 200, Number of Men = 113\)
\(Increase = 68.\)

I think the main takeaway for this problem is to separate the "real" working rate and the planned working rate and understand them correctly. I was making a mistake by assuming the added workers will work at the planned rate and got the question wrong!

The rate for 45 men is 2.5/100 = 25/1000 = 1/40.

In order to complete the remaining 12.5 km of the road in 200 days, the rate of the men must be:

12.5/200 = 125/2000 = 1/16

If we let n = the new number of men we can create the proportion:

45/(1/40) = n/(1/16)

1,800 = 16n

n = 112.5

Since we cannot have a decimal number of men, the new number of men must be 113, so we must need 113 - 45 = 68 extra men.

Answer: D

Thanks for your great explanation.
Can you explain that why you put the two ratios equal to each other--->45/(1/40) = n/(1/16)
I didn't get this part.



quote="JeffTargetTestPrep"]
The rate for 45 men is 2.5/100 = 25/1000 = 1/40.

In order to complete the remaining 12.5 km of the road in 200 days, the rate of the men must be:

12.5/200 = 125/2000 = 1/16

If we let n = the new number of men we can create the proportion:

45/(1/40) = n/(1/16)

1,800 = 16n

n = 112.5

Since we cannot have a decimal number of men, the new number of men must be 113, so we must need 113 - 45 = 68 extra men.

Answer: D[/quote]

Let's say 2.5km = 1 and 15km = 6 (for simplicity sake, the proportion is maintained).

> 45M ---> 100 days ---> 1 (2.5km)
> In 1 day ----> 1/100 (this is the rate of 45 Men)
> 1M ---------------------> 1/100x45 = 1/4500

There's 12.5km left = 5 (by our simplification).

We know that Work = rate x time

So we need to find how many more men we need (45 + X) to complete the extra 5 (Work), at a 1/4500 rate in 200 days (time).

> 5 = (45 + X) x (1/4500) x 200
> 2X = 135 = 67.5 Aprox. 68

To do 2.5 Kms, the Man Days required = 45 * 10 = 4500

Therefore to do 12.5 km, MD required = \(\frac{12.5 \space * \space 4500}{2.5} = 22,500 \) Man Days

This 22,500 Man days has to be completed in the remaining 200 days, with extra men over and above the 45.

Let the excess men = x


Therefore (x + 45) * 200 = 22500

x + 45 = 112.5

x = 67.5 \(\approx\) 68 men



Option D

Arun Kumar

total work 15 km
total days 300
men ; 45
work done 2.5 km ; left with 12.5 km
m1*t1/w1 = m2*t2/w2
45*100/ 2.5 = x * 200 / 12.5
x= 112
112.5-45 ; 67.5 ~68 men more required
option D