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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