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# A and B together complete a piece of job in 10 days, B and C together

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Math Expert
Joined: 02 Sep 2009
Posts: 41873

Kudos [?]: 128621 [2], given: 12180

A and B together complete a piece of job in 10 days, B and C together [#permalink]

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14 Aug 2017, 22:19
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Question Stats:

69% (02:08) correct 31% (01:21) wrong based on 48 sessions

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A and B together complete a piece of job in 10 days, B and C together complete the same piece of job in 15 days, whereas A and C together complete it in 8 days. How many days will it take to complete the job if all of them work together?

A. $$3 \frac{3}{7}$$

B. $$6 \frac{6}{7}$$

C. $$7$$

D. $$7 \frac{23}{35}$$

E. $$7 \frac{6}{7}$$
[Reveal] Spoiler: OA

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Kudos [?]: 128621 [2], given: 12180

Senior Manager
Joined: 25 Feb 2013
Posts: 393

Kudos [?]: 164 [2], given: 31

Location: India
GPA: 3.82
A and B together complete a piece of job in 10 days, B and C together [#permalink]

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14 Aug 2017, 22:34
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Bunuel wrote:
A and B together complete a piece of job in 10 days, B and C together complete the same piece of job in 15 days, whereas A and C together complete it in 8 days. How many days will it take to complete the job if all of them work together?

A. $$3 \frac{3}{7}$$

B. $$6 \frac{6}{7}$$

C. $$7$$

D. $$7 \frac{23}{35}$$

E. $$7 \frac{6}{7}$$

(A+B)'s 1 day job = $$\frac{1}{10}$$
(B+C)'s 1 day job = $$\frac{1}{15}$$
(A+C)'s 1 day job = $$\frac{1}{8}$$

Adding the three equations we get -
$$2$$(A+B+C)'s 1 day job = $$\frac{1}{10}+\frac{1}{15}+\frac{1}{8} = \frac{35}{120}$$
or (A+B+C)'s 1 day job = $$\frac{35}{120}*\frac{1}{2}$$ $$=\frac{7}{48}$$
Hence time taken by All to complete the job = $$\frac{48}{7}$$ = $$6 \frac{6}{7}$$

Option B

Last edited by niks18 on 14 Aug 2017, 23:05, edited 1 time in total.

Kudos [?]: 164 [2], given: 31

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Joined: 26 Feb 2016
Posts: 1449

Kudos [?]: 592 [1], given: 16

Location: India
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A and B together complete a piece of job in 10 days, B and C together [#permalink]

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14 Aug 2017, 22:58
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If A and B can together do the piece of work in $$10(2*5)$$ days, B and C do the work in $$15(3*5)$$ days
, and A and C do the work in $$8(2^3)$$ days

Let us assume the work to be $$120(2^3 * 3 * 5)$$ units.

Therefore A & B's combined rate is 12 units, B & C's combined rate is 8 units, and A & C's combined rate is 15 units.

Together they would do half of 35(12+8+15) units in a day.
So their combined rate is $$\frac{35}{2}$$ units per day.

In order to finish 120 units at that rate, it would require $$120 * (\frac{2}{35}) = \frac{120*2}{35} = \frac{24*2}{7} = \frac{48}{7} = 6\frac{6}{7}$$ days(Option B)
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Kudos [?]: 592 [1], given: 16

A and B together complete a piece of job in 10 days, B and C together   [#permalink] 14 Aug 2017, 22:58
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