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# 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  [#permalink]

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22 May 2011, 04:56
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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
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Re: An engineer undertakes a project to build a road 15 km long in 300 day  [#permalink]

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22 May 2011, 06:56
1
ramkryp wrote:
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

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
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Re: An engineer undertakes a project to build a road 15 km long in 300 day  [#permalink]

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22 May 2011, 10:03
1
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
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Re: An engineer undertakes a project to build a road 15 km long in 300 day  [#permalink]

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23 May 2011, 10:48
3
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

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Re: An engineer undertakes a project to build a road 15 km long in 300 day  [#permalink]

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23 May 2011, 22:33
1
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.
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Re: An engineer undertakes a project to build a road 15 km long in 300 day  [#permalink]

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23 May 2011, 22:49
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

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An engineer undertakes a project to build a road 15 km long in 300 day  [#permalink]

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05 Feb 2016, 16:22
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
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Re: An engineer undertakes a project to build a road 15 km long in 300 day  [#permalink]

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25 Mar 2016, 04:57
1
(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
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Re: An engineer undertakes a project to build a road 15 km long in 300 day  [#permalink]

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25 Mar 2016, 18:39
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
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Re: An engineer undertakes a project to build a road 15 km long in 300 day  [#permalink]

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27 Mar 2016, 00:47
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
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Re: An engineer undertakes a project to build a road 15 km long in 300 day  [#permalink]

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27 Mar 2016, 06:45
vyassaptarashi wrote:
ramkryp wrote:
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

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

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.?
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An engineer undertakes a project to build a road 15 km long in 300 day  [#permalink]

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Updated on: 08 Feb 2018, 21:04
ramkryp wrote:
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

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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Originally posted by Jamil1992Mehedi on 04 Feb 2018, 23:58.
Last edited by Jamil1992Mehedi on 08 Feb 2018, 21:04, edited 1 time in total.
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Re: An engineer undertakes a project to build a road 15 km long in 300 day  [#permalink]

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05 Feb 2018, 00:21
bethebest wrote:
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.?

Seems correct to me.
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Re: An engineer undertakes a project to build a road 15 km long in 300 day  [#permalink]

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05 Feb 2018, 00:47
1
ramkryp wrote:
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

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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Re: An engineer undertakes a project to build a road 15 km long in 300 day  [#permalink]

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06 Feb 2018, 05:05
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!
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Re: An engineer undertakes a project to build a road 15 km long in 300 day  [#permalink]

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08 Feb 2018, 16:44
1
ramkryp wrote:
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

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.

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Re: An engineer undertakes a project to build a road 15 km long in 300 day  [#permalink]

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11 Feb 2018, 10:18
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"]
ramkryp wrote:
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

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.

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An engineer undertakes a project to build a road 15 km long in 300 day  [#permalink]

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24 Feb 2018, 00:00
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
An engineer undertakes a project to build a road 15 km long in 300 day &nbs [#permalink] 24 Feb 2018, 00:00
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