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A can do 1/3 of the work in 5 days and B can do 2/5 of the work in 10

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A can do 1/3 of the work in 5 days and B can do 2/5 of the work in 10  [#permalink]

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New post 22 Oct 2017, 19:34
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79% (01:17) correct 21% (01:18) wrong based on 71 sessions

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A can do \(\frac{1}{3}\) of the work in 5 days and B can do \(\frac{2}{5}\) of the work in 10 days. In how many days both A and B together can do the work?

A) 7\(\frac{3}{4}\)

B) 8\(\frac{4}{5}\)

C) 9\(\frac{3}{8}\)

D) 10

E) 12

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A can do 1/3 of the work in 5 days and B can do 2/5 of the work in 10  [#permalink]

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New post 23 Oct 2017, 00:10
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varun4s wrote:
A can do \(\frac{1}{3}\) of the work in 5 days and B can do \(\frac{2}{5}\) of the work in 10 days. In how many days both A and B together can do the work?

A) 7\(\frac{3}{4}\)

B) 8\(\frac{4}{5}\)

C) 9\(\frac{3}{8}\)

D) 10

E) 12

This approach looks time-consuming. It isn't. Find and add rates. Work is 1; flip the rate to get the number of days it would take A and B, working together, to finish.

RATES: To find rates, use \(\frac{Work}{time} = rate\)

A's rate, in \(\frac{Work}{days}\):
\(\frac{(\frac{1}{3})}{5}=(\frac{1}{3} * \frac{1}{5})=\frac{1}{15}\)

B's rate:
\(\frac{(\frac{2}{5})}{10}=(\frac{2}{5} * \frac{1}{10})=\frac{2}{50}=\frac{1}{25}\)

Add rates of A, \(\frac{1}{15}\), and B, \(\frac{1}{25}\), with LCM of 150.
COMBINED RATE of A and B:

\((\frac{10}{150} + \frac{6}{150})=\frac{16}{150} = \frac{8}{75}\)

TIME: How many days does it take them, working together, to finish the job?
Job = 1
When work is 1, rate and time are inversely proportional.

Invert the combined rate, \(\frac{8}{75}\), to get the time: \(\frac{75}{8} = 9\frac{3}{8}\) days, OR

\(\frac{Work}{Rate} = time\)

\(\frac{1}{(\frac{8}{75})}= 1 * \frac{75}{8} =9\frac{3}{8}\)

Answer C
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Re: A can do 1/3 of the work in 5 days and B can do 2/5 of the work in 10  [#permalink]

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New post 26 Oct 2017, 15:33
varun4s wrote:
A can do \(\frac{1}{3}\) of the work in 5 days and B can do \(\frac{2}{5}\) of the work in 10 days. In how many days both A and B together can do the work?

A) 7\(\frac{3}{4}\)

B) 8\(\frac{4}{5}\)

C) 9\(\frac{3}{8}\)

D) 10

E) 12


A’s rate is (1/3)/5 = 1/15 and B’s rate is (2/5)/10 = 2/50 = 1/25.

Their combined rate is 1/15 + 1/25 = 5/75 + 3/75 = 8/75.

Thus, the time it takes the two machines to complete the job is 1/(8/75) = 75/8 = 9 3/8 days.

Answer: C
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Re: A can do 1/3 of the work in 5 days and B can do 2/5 of the work in 10 &nbs [#permalink] 26 Oct 2017, 15:33
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