Question

8. A can do (1/3) of a work in 5 days and B can do (2/5) of
the work in 10 days. In how many days both A and B
together can do the work?
3
4
a) 7days b) 9 days c) 83 days d) 10 days

Answer 1

Answer:

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Answer 2

$\large\boxed{\text{Basic Concepts}}$

The formula for work:-

$\hookrightarrow \large\boxed{\text{Work rate}=\dfrac{\text{Amount of work}}{\text{Time}}}$

$\large\text{\underline{Solution}}$

Since A can do $\dfrac{1}{3}$ of work in 5 days, A can do $\dfrac{1}{15}$ of work each day.

Since B can do $\dfrac{2}{5}$ of work in 10 days, B can do $\dfrac{1}{25}$ of work each day.

Then, together A and B do $\dfrac{1}{15}+\dfrac{1}{25}=\dfrac{8}{75}$ of work each day.

According to the formula, we find values in the given conditions.

• $\text{(Amount of work)}=1\ \text{work}$
• $\text{(Time)}=x\ \text{day(s)}$
• $\text{Work rate}=\dfrac{8}{75}\ \text{work/day}$

$\hookrightarrow \dfrac{8}{75}=\dfrac{1}{x}$

$\hookrightarrow x=\dfrac{75}{8}$

Hence,

• $\text{(Time)}=\dfrac{75}{8}\ \text{days}$

Both workers can do the work in $\dfrac{75}{8}$ days. So, the answer is not in the options.