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' GlobalAttachment:

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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 aloneA 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 hoursB 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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