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A can do a work in 15 days and B can do the same work in 20 days. If..

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varun4s
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A can do a work in 15 days and B can do the same work in 20 days. If.. [#permalink] New post   11 Oct 2017, 19:11
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A can do a work in 15 days and B can do the same work in 20 days. If they work together for 4 days, then the fraction of work that has left is:

A) \(\frac{1}{4}\)

B) \(\frac{1}{5}\)

C)\(\frac{1}{10}\)

D) \(\frac{7}{15}\)

E) \(\frac{8}{15}\)


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E
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A can do a work in 15 days and B can do the same work in 20 days. If.. [#permalink] New post   12 Oct 2017, 08:26
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varun4s wrote:
A can do a work in 15 days and B can do the same work in 20 days. If they work together for 4 days, then the fraction of work that has left is:

A) \(\frac{1}{4}\)

B) \(\frac{1}{5}\)

C)\(\frac{1}{10}\)

D) \(\frac{7}{15}\)

E) \(\frac{8}{15}\)

Kindly hit kudos if my post helps!

This question has a wrinkle: it asks for work remaining, not work finished.

A's rate, W/day = \(\frac{1}{15}\)

B's rate, W/day = \(\frac{1}{20}\)

Add rates with LCM of 60. Together, their rate is \(\frac{4}{60} + \frac{3}{60}\) =\(\frac{7}{60}\)

They work together at this rate for t = 4 days. \(rt=W\)

They finish: \((\frac{7}{60} * 4) =\frac{28}{60} =\frac{7}{15}\)

Fraction of work that is left

(\(1 -\frac{7}{15}) =(\frac{15}{15} -\\
\frac{7}{15}) =\frac{8}{15}\)

Answer E
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A can do a work in 15 days and B can do the same work in 20 days. If.. [#permalink] New post   16 Oct 2017, 20:59
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In 1 day, A finishes 1/15 job
In 1 day, B finishes 1/20 job
Totally, in 1 day, both A and B finish (1/15 +1/20) = 7/60 job

In 4 days, both A and B finish 4x7/60 = 7/15 job.
After 4 days, the remaining job is 1-7/15 = 8/15 job.

Answer is E

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Re: A can do a work in 15 days and B can do the same work in 20 days. If.. [#permalink] New post   11 Oct 2017, 19:37
1- [1/15+1/20]*4
= 1-7/15
=8/15
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Re: A can do a work in 15 days and B can do the same work in 20 days. If.. [#permalink] New post   16 Oct 2017, 16:57
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varun4s wrote:
A can do a work in 15 days and B can do the same work in 20 days. If they work together for 4 days, then the fraction of work that has left is:

A) \(\frac{1}{4}\)

B) \(\frac{1}{5}\)

C)\(\frac{1}{10}\)

D) \(\frac{7}{15}\)

E) \(\frac{8}{15}\)


We use the formula work = rate x time. The work completed in 4 days is:

(1/15) x 4 + (1/20) x 4 = 4/15 + 4/20 = 16/60 + 12/60 = 28/60 = 7/15

In 4 days, we see that 7/15 of the job has been completed. So, 1 - 7/15 = 15/15 - 7/15 = 8/15 of the job is left to be completed.

Answer: E
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Re: A can do a work in 15 days and B can do the same work in 20 days. If.. [#permalink]
16 Oct 2017, 16:57
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