Question: 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?

1. \(7\frac{3}{4}\)
2. \(8\frac{4}{5}\)
3. \(9\frac{3}{8}\)
4. 10
5. 12

“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?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer:

Approach Solution (1):

As we know that \(rate=\frac{work}{time}\)

A’s rate in: \(\frac{work}{days}: \frac{1}{\frac{3}{5}}=\frac{1}{3}*\frac{1}{5}=\frac{1}{15} \)

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

Add rates of A, \(\frac{1}{15}\), and B, \(\frac{1}{25}\), with LCM of 75

Combined rate of A and B =\(\frac{5}{75}+\frac{3}{75}=\frac{8}{75}\)

Time: How many days does it take them, working together, to finish the job?

Job:

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

Correct option: C

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