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Jamshid can paint a fence in 50 percent less time than Taimour can whe

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Jamshid can paint a fence in 50 percent less time than Taimour can whe [#permalink]

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New post 23 Sep 2015, 22:43
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D
E

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  25% (medium)

Question Stats:

76% (01:15) correct 24% (02:01) wrong based on 169 sessions

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Jamshid can paint a fence in 50 percent less time than Taimour can when each works alone. When they work together, they can paint the fence in 8 hours. How long would it take Taimour to paint the fence alone?

(A) 6 hours
(B) 8 hours
(C) 14 hours
(D) 24 hours
(E) 32 hours

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Re: Jamshid can paint a fence in 50 percent less time than Taimour can whe [#permalink]

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New post 24 Sep 2015, 00:00
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Let J+T finish work in 8 hrs.

Let us assume total work = 80 units

Hence J+T can finish 10 units/hr

Now given that rate of work of J = 2 x rate of work of T

Hence rate of work of J= 20/3 units/hr and rate of work of T = 10/3 units/hr

Hence time taken by T = 80x3/10 = 24 hours . Option D.

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Jamshid can paint a fence in 50 percent less time than Taimour can whe [#permalink]

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New post 24 Sep 2015, 00:57
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Time taken by Taimour (T) to finish the work be x hrs, so the amount of work T can do in 1 hr = 1/x
=> Time taken by Jamshid (J) would be x/2 hrs, and the amount of work J can do in 1 hr = 2/x

When working together they can complete the work in 8 hours, so the work completed in 1 hr = 1/8
=> 1/x + 2/x = 1/8
=> 3/x = 1/8
=> x = 24

Time taken by Taimour to paint the fence alone is 24 hours. Option D
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Re: Jamshid can paint a fence in 50 percent less time than Taimour can whe [#permalink]

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New post 24 Sep 2015, 07:53
1
Bunuel wrote:
Jamshid can paint a fence in 50 percent less time than Taimour can when each works alone. When they work together, they can paint the fence in 8 hours. How long would it take Taimour to paint the fence alone?

(A) 6 hours
(B) 8 hours
(C) 14 hours
(D) 24 hours
(E) 32 hours

Kudos for a correct solution.


Let x be the time taken by jamshid to paint a fence.Then time taken by taimour will be 2x
They take 8 hours to paint a fence together.So their 1 hour work will be 1/8

or \(\frac{1}{x}+\frac{1}{2x}=\frac{1}{8}\)

or \(\frac{3}{2x}=\frac{1}{8}\)

or \(x=12\)

Time taken by taimour is 2x or 2*12 =24

Answer:- D
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Re: Jamshid can paint a fence in 50 percent less time than Taimour can whe [#permalink]

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New post 24 Sep 2015, 09:59
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I believe the answer is D. Please see below for explanation.


if Jamshid can paint a dence in 50 percent less time then Taimour we can infer the following rate J = 2T

if working together they can do the job in 8 hours we can infer 1 = 2T+T * 8 => 1/24

Working alone Taimour can do the job in 1 = 1/24 * hours => 24


Answer D
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Jamshid can paint a fence in 50 percent less time than Taimour can whe [#permalink]

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New post 03 Sep 2017, 06:57
1
Bunuel wrote:
Jamshid can paint a fence in 50 percent less time than Taimour can when each works alone. When they work together, they can paint the fence in 8 hours. How long would it take Taimour to paint the fence alone?

(A) 6 hours
(B) 8 hours
(C) 14 hours
(D) 24 hours
(E) 32 hours

Kudos for a correct solution.

Let's Taimur can do the work in X hours, Jamshid does the work in .5 x hours. so, their respective rate of doing the work is 1/x and 1/.5x. If they work together, their rate of work has to be 1/8
so,
1/x+1/.5x= 1/8
or, x=24
Option D is the answer.
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Jamshid can paint a fence in 50 percent less time than Taimour can whe   [#permalink] 03 Sep 2017, 06:57
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Jamshid can paint a fence in 50 percent less time than Taimour can whe

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