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When A works alone, it takes 14hrs, and when A works with B together,

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When A works alone, it takes 14hrs, and when A works with B together, [#permalink]

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New post 09 Aug 2017, 04:29
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When A works alone, it takes 14hrs, and when A works with B together, it takes 10hrs. How many hours does it take B to work alone?

A. 30hrs
B. 33hrs
C. 35hrs
D. 37hrs
E. 40hrs
[Reveal] Spoiler: OA

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When A works alone, it takes 14hrs, and when A works with B together, [#permalink]

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New post 09 Aug 2017, 04:39
MathRevolution wrote:
When A works alone, it takes 14hrs, and when A works with B together, it takes 10hrs. How many hours does it take B to work alone?

A. 30hrs
B. 33hrs
C. 35hrs
D. 37hrs
E. 40hrs


Hi,

Note: Consider total amount of work as LCM of no. of hours required by different persons.

In this case, let's assume total amount of work = 70 units (LCM (14,10) = 70)

Rate of A work = 70/14 = 5 units/hr

Rate of A+B work = 70/10 = 7 units/hr

Rate of B work = 7 - 5 = 2 units/hr

The total amount of time required to complete the work by B = 70/2 = 35 hrs.

Answer: (C)

Thanks.

Last edited by ganand on 10 Aug 2017, 00:21, edited 1 time in total.

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Re: When A works alone, it takes 14hrs, and when A works with B together, [#permalink]

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New post 09 Aug 2017, 05:20
Lets arrange the Information and assume that 1 unit of work needs to be done.

Work = Rate * Time
A: 1 = * 14
B: 1 = * T
A+B: 1 = * 10

Now we fill in what we can deduct

Work = Rate * Time
A: 1 = 1/14 * 14
B: 1 = 1/T * T
A+B: 1 = 1/10 * 10

What we need is T. If we add the rates of A and B we get the combined rate A+B.

(1/14) + (1/T) = (1/10)
=>(T+14 / 14T) = (1/10)
=>T+14 = (14T/10)
=>10T + 140 = 14T
=>140 = 4T
=>T = 35

Answer C

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Re: When A works alone, it takes 14hrs, and when A works with B together, [#permalink]

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New post 09 Aug 2017, 09:03
MathRevolution wrote:
When A works alone, it takes 14hrs, and when A works with B together, it takes 10hrs. How many hours does it take B to work alone?

A. 30hrs
B. 33hrs
C. 35hrs
D. 37hrs
E. 40hrs

Let the total work be = 70

Efficiency of A = 5
Efficiency of A + B = 7
So, Efficiency of B = 2

So, Time taken by B to work alone is \(\frac{70}{2}\) = \(35\) hours..

Thus, answer must be (C)
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When A works alone, it takes 14hrs, and when A works with B together, [#permalink]

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New post 09 Aug 2017, 09:10
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MathRevolution wrote:
When A works alone, it takes 14hrs, and when A works with B together, it takes 10hrs. How many hours does it take B to work alone?

A. 30hrs
B. 33hrs
C. 35hrs
D. 37hrs
E. 40hrs

There are a few ways to solve these problems. If possible, I find adding rates the easiest.

"It" is one job, or one unit of work.

(Rate of A and B together) - (rate of A) = (rate of B)

\(\frac{1}{10}\) - \(\frac{1}{14}\) =\(\frac{(14 - 10)}{140}\)

= \(\frac{4}{140}\) = \(\frac{1}{35}\) --> B's rate

When work unit is one, flip the rate to get the time: 1/(1/35) = 35

Answer C

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Re: When A works alone, it takes 14hrs, and when A works with B together, [#permalink]

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New post 09 Aug 2017, 19:39
Abhishek009 wrote:
MathRevolution wrote:
When A works alone, it takes 14hrs, and when A works with B together, it takes 10hrs. How many hours does it take B to work alone?

A. 30hrs
B. 33hrs
C. 35hrs
D. 37hrs
E. 40hrs

Let the total work be = 70

Efficiency of A = 5
Efficiency of A + B = 7
So, Efficiency of B = 2

So, Time taken by B to work alone is \(\frac{70}{2}\) = \(35\) hours..

Thus, answer must be (C)


Hello,
How do you assume A= 5?
Thank you very much

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Re: When A works alone, it takes 14hrs, and when A works with B together, [#permalink]

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New post 09 Aug 2017, 20:04
Hi pclawong,

It is not so much as assumption in this case.
Here, the total units of work is 70 units and since A (when working alone) does the work in 14 hours,
A's efficieny is 70/14 = 5 units
Similarly, Since both do the work in 10 hours, their combined efficiency is 7 units.

This makes the efficiency of B(2 units), and the time it takes him to complete the work 35 hours(Option C)

Hope that helps you!
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Re: When A works alone, it takes 14hrs, and when A works with B together, [#permalink]

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New post 11 Aug 2017, 01:03
==> For work rate questions, you solve “together and alone” reciprocally. It takes A 14hrs alone, and if you set the hours it took B to work alone as B hrs, from \((\frac{1}{14})+(\frac{1}{B})=\frac{1}{10}\) and \(\frac{1}{B}=(\frac{1}{10})-(\frac{1}{14})=\frac{1}{35}\), you get \(B=35\).

The answer is C.
Answer: C
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Re: When A works alone, it takes 14hrs, and when A works with B together,   [#permalink] 11 Aug 2017, 01:03
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