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Working independently, Tina can do a certain job in 12 hours

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Working independently, Tina can do a certain job in 12 hours  [#permalink]

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27 Nov 2018, 09:06
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Difficulty:

5% (low)

Question Stats:

86% (01:24) correct 14% (02:02) wrong based on 90 sessions

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Working independently, Tina can do a certain job in 12 hours. Working independently, Ann can do the same job in 9 hours. If Tina works independently at the job for 8 hours and then Ann works independently, how many hours will it take Ann to complete the remainder of the job?

(A) 2/3
(B) 3/4
(C) 1
(D) 2
(E) 3

Project PS Butler : Question #43

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Re: Working independently, Tina can do a certain job in 12 hours  [#permalink]

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27 Nov 2018, 11:05
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HKD1710 wrote:
Working independently, Tina can do a certain job in 12 hours. Working independently, Ann can do the same job in 9 hours. If Tina works independently at the job for 8 hours and then Ann works independently, how many hours will it take Ann to complete the remainder of the job?

(A) 2/3
(B) 3/4
(C) 1
(D) 2
(E) 3

Project PS Butler : Question #43

Work done by Tina $$\frac{8}{12}$$

Work left to be done $$\frac{1}{3}$$

Ann`s Rate $$\frac{1}{9}$$

To find how much time it will take for Ann to complete remainder of job divide work by rate

i.e $$\frac{\frac{1}{3}}{\frac{1}{9}}$$ = $$\frac{1}{3} *\frac{9}{1}$$ = $$3$$

IMO: E
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Re: Working independently, Tina can do a certain job in 12 hours  [#permalink]

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10 Feb 2019, 00:54
HKD1710 wrote:
Working independently, Tina can do a certain job in 12 hours. Working independently, Ann can do the same job in 9 hours. If Tina works independently at the job for 8 hours and then Ann works independently, how many hours will it take Ann to complete the remainder of the job?

(A) 2/3
(B) 3/4
(C) 1
(D) 2
(E) 3

Rate of R = W/12 = 3 units/hr
Rate of A = W/9 = 4 units/hr

Let W = 36 units

R works for 8 hrs means work done = 24 units

Remaining work = 12 units

A works for 3 hrs for the remaining 12 units
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Working independently, Tina can do a certain job in 12 hours  [#permalink]

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Updated on: 13 Feb 2019, 22:28

Solution

Given:
• Working independently, Tina can do a certain job in 12 hours.
• Working independently, Ann can do the same job in 9 hours.
• Tina works independently at the job for 8 hours and then Ann works independently.

To find:
• The time taken by Ann, to complete the remainder of the job.

Approach and Working:
Let us assume the total job = LCM (12, 9) = 36 units

• 1-hour job of Tina = $$\frac{36}{12}$$ = 3 units
• 1-hour job of Ann = $$\frac{36}{9}$$ = 4 units

As Tina works for the first 8 hours, the amount of work done by Tina = 3 x 8 = 24 units

Hence, remaining job = 36 – 24 = 12 units
Therefore, the time taken by Ann = $$\frac{12}{4}$$ = 3 hours

Hence, the correct answer is option E.

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Originally posted by EgmatQuantExpert on 10 Feb 2019, 05:35.
Last edited by EgmatQuantExpert on 13 Feb 2019, 22:28, edited 1 time in total.
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Re: Working independently, Tina can do a certain job in 12 hours  [#permalink]

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10 Feb 2019, 05:40
HKD1710 wrote:
Working independently, Tina can do a certain job in 12 hours. Working independently, Ann can do the same job in 9 hours. If Tina works independently at the job for 8 hours and then Ann works independently, how many hours will it take Ann to complete the remainder of the job?

(A) 2/3
(B) 3/4
(C) 1
(D) 2
(E) 3

Project PS Butler : Question #43

rate of Tina = 1/12
Rate of Ann = 1/9

so work done by tina n 8 hrs
x/12 * 8 = 2x/3
left = x/3
so Ann would take
x/3 * 9 = 3 hrs
x = 1
IMO E
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Re: Working independently, Tina can do a certain job in 12 hours   [#permalink] 10 Feb 2019, 05:40
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