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

Question

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

A. 43
B. 45
C. 55
D. 68
E. 60

hussi9 · Accepted Answer

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

jpvemula · Answer

(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

vyassaptarashi · Answer

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

sudhir18n · Answer

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

amit2k9 · Answer

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.

subhashghosh · Answer

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

gracie · Answer

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

gracie · Answer

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

gps5441 · Answer

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

Posted from my mobile device

bethebest · Answer

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.?

Jamil1992Mehedi · Answer

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

regards, Jamil_Mehedi

saswata4s · Answer

Seems correct to me.

rahul16singh28 · Answer

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.

hoang221 · Answer

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!

JeffTargetTestPrep · Answer

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

sananoor · Answer

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

raphael.anp · Answer

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

CrackverbalGMAT · Answer

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

Archit3110 · Answer

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

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

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

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