Question

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

• A. $7_4^3$
• B. $8_5^4$
• C. $9_8^3$
• D. 10 days

Answer 1

Answer: (C)

$9_8^3$

A's rate in Work days: $\left(\frac{1}{3\ast 5}\right)=(\frac{1}{3}\ast \frac{1}{3})=\frac{1}{15}$

B's rate, in Work days: $\left(\frac{2}{5\ast 10}\right)=(\frac{2}{5}\ast \frac{1}{10})=\frac{2}{50}=\frac{1}{25}$

LCM of rates of A, $\frac{1}{15}$ , and B, $\frac{1}{25}$ is $150.$

combine rate of A and B:$(\frac{10}{150}+\frac{6}{150})=\frac{16}{150}=\frac{8}{75}$

$\frac{work}{rate}=time$

$⟹\frac{1}{\frac{8}{75}}=time$

$⟹time=\frac{75}{8}=9\frac{3}{8}$

So, option (c) is correct.