We can look at it this way.

Work done depends on 2 things in this problems. Number of men and the days for which they work.
i.e. Direct proportion

45 MEN working for 100 DAYS complete 2.5 Unit of WORK
So How many Men (X) will be needed to complete 12.5 Unit of WORK in 200 DAYS.

Equation can be written as
(45*100 )/ (X*200) = 2.5 / 12.5

Solve for X

Answer is X-45
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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

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
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(i) It took 100 days for 45 men to complete 2.5 Km . i.e 4500 mandays for 2.5 km
(ii) For remaining 12.5 km no. of mandays = (12.5/2.5)* 4500 = 22500 mandays
(iii) Remaining no. of days = 200

From (ii) & (iii) no. of men required = 22500/200 = 112.5 ~ 113
So no. of extra men= 113-45 =68

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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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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If you like my way of clarification, please give me one Kudos
regards,
Jamil_Mehedi

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