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A contractor undertakes to dig a canal 12km long in 350 days and emplo

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A contractor undertakes to dig a canal 12km long in 350 days and emplo  [#permalink]

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New post 25 Jan 2017, 12:15
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Question Stats:

61% (03:17) correct 39% (03:13) wrong based on 74 sessions

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A contractor undertakes to dig a canal 12km long in 350 days and employs 45 men.After 200 days he finds that only 4.5km of canal has been completed.
Find the number of extra men he must employ to finish the work in time??

A. 53
B. 55
C. 43
D. 59
E. 48


Source: quicker maths
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Re: A contractor undertakes to dig a canal 12km long in 350 days and emplo  [#permalink]

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New post 25 Jan 2017, 12:25
4.5 km in 200 days by 45 men
now remaining 7.5 km in 150 days by 45+x men
200*45/4.5 =(45+x)*150/7.5
on solving this we get x=55 so 55 men extra are required

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Re: A contractor undertakes to dig a canal 12km long in 350 days and emplo  [#permalink]

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New post 25 Jan 2017, 22:30
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A contractor undertakes to dig a canal 12km long in 350 days and employs 45 men.After 200 days he finds that only 4.5km of canal has been completed.
Find the number of extra men he must employ to finish the work in time??

A. 53
B. 55
C. 43
D. 59
E. 48

let x=km per man per day
45*x*200=4.5 km
x=1/2000 km
let y=additional men needed
(45+y)*1/2000*150=7.5 km
y=55
B
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Re: A contractor undertakes to dig a canal 12km long in 350 days and emplo  [#permalink]

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New post 27 Jan 2017, 04:06
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Hi Rohit8865,

This is a group work question. Whenever you encounter a group work question, you can make use of the following universal formula for group work.

(M1D1H1)/W1 = (M2D2H2)/W2

Where M1 and M2 are men
D1 and D2 are days
H1 and H2 are hours and
W1 and W2 are the work done


Here since we have 3 quantities M, D and W, we use the formula (M1D1)/W1 = (M2D2)/W2

Since 45 men take 200 days to dig 4.5 km of a canal, we need to find how many more men are required to complete the remaining 7.5 km of the canal in 150 days.

M1 = 45
D1 = 200
W1 = 4.5
M2 = ?
D2 = 150
W2 = 7.5

Substituting in (M1D1)/W1 = (M2D2)/W2 we get

(45 * 200)/4.5 = (M2 * 150)/7.5

Simplifying we get M2 = 100.

Since we need to find how many more men are required, the answer will be 100 - 45 = 55.

Hope this helps!

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Re: A contractor undertakes to dig a canal 12km long in 350 days and emplo  [#permalink]

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New post 30 Jan 2017, 16:35
rohit8865 wrote:
A contractor undertakes to dig a canal 12km long in 350 days and employs 45 men.After 200 days he finds that only 4.5km of canal has been completed.
Find the number of extra men he must employ to finish the work in time??

A. 53
B. 55
C. 43
D. 59
E. 48


We can determine that the rate of the 45 men is 4.5/200 = 45/2,000 = 9/400.

We need to determine how many more men, working at the same constant rate must be used to dig another 7.5 km in 150 days. Thus, the men need to work at a rate of 7.5/150 = 75/1,500 = 1/20.

We can use a proportion to determine the total number of men needed to do the remainder of the job in the allotted time.

(x men)/(1/20) = (45 men)/(9/400)

9x/400 = 45/20

9x/400 = 9/4

9x/400 = 900/400

9x = 900

x = 100

Thus, the contractor needs to have a total of 100 men to complete the job on time. Since he already has 45 men, he needs to hire 100 - 45 = 55 more men.

Answer: B
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Re: A contractor undertakes to dig a canal 12km long in 350 days and emplo  [#permalink]

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New post 22 Apr 2018, 04:37
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Re: A contractor undertakes to dig a canal 12km long in 350 days and emplo &nbs [#permalink] 22 Apr 2018, 04:37
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