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A does a work in 8hrs, B does the same owrk in 16 hrs

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A does a work in 8hrs, B does the same owrk in 16 hrs  [#permalink]

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New post 22 Nov 2017, 13:43
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A
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C
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Difficulty:

  15% (low)

Question Stats:

89% (02:58) correct 11% (03:36) wrong based on 36 sessions

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A does a work in 8hrs, B does the same work in 16 hrs and C does it in 12hrs. A starts working and is joined by B after 2hrs. After 3hrs of working together,A leaves and C joins. How much more time will it take to complete the work if B and C continue to work until it's over?

1.12 hr
2. 15/16 hr
3.9/7 hr
4. 5 hr
5. 16 hr

Source: Experts' Global
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A does a work in 8hrs, B does the same owrk in 16 hrs  [#permalink]

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New post 22 Nov 2017, 15:52
Sangeeta2018 wrote:
A does a work in 8hrs, B does the same work in 16 hrs and C does it in 12hrs. A starts working and is joined by B after 2hrs. After 3hrs of working together,A leaves and C joins. How much more time will it take to complete the work if B and C continue to work until it's over?

1.12 hr
2. 15/16 hr
3.9/7 hr
4. 5 hr
5. 16 hr

Source: Experts' Global

Attachment:
wrt3.png
wrt3.png [ 23.8 KiB | Viewed 371 times ]

To say this answer is arithmetic-intensive is to radically understate the case. ;)

Work rates:

A's rate: \(\frac{1}{8}\)

B's rate: \(\frac{1}{16}\)

C's rate: \(\frac{1}{12}\)

rate of A + B: (\(\frac{1}{8} + \frac{1}{16}) = \frac{3}{16}\)

rate of B + C:\((\frac{1}{16} + \frac{1}{12}) = (\frac{3}{48} + \frac{4}{48}) = \frac{7}{48}\)

Segment 1 - A works alone

A works alone for two hours. rate * time = Work

\(\frac{1}{8}* 2 = \frac{1}{4}\) work finished. Work remaining: \(\frac{3}{4}\)

Segment 2: A and B work together for 3 hours

B joins A for 3 hours.

Rate of \(A + B =\frac{3}{16}\)

Work finished? rate * time = Work

\(\frac{3}{16} * 3 hrs = \frac{9}{16}\) work is finished

Work remaining?

\((\frac{3}{4}- \frac{9}{16}) = (\frac{12}{16} - \frac{9}{16}) = \frac{3}{16}\)

Work remaining: \(\frac{3}{16}\)

Segment 3: A leaves, C joins B -- how long to finish whatever work is left?

A leaves, C joins. How long for B and C to finish? \(\frac{Work}{rate} = time\)

Rate of \(B + C =\frac{7}{48}\)

\(\frac{\frac{3}{16}}{\frac{7}{48}}\) = \((\frac{3}{16} * \frac{48}{7}) = \frac{9}{7} hrs\)

Answer C
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A does a work in 8hrs, B does the same owrk in 16 hrs &nbs [#permalink] 22 Nov 2017, 15:52
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