Question : A can do a piece of work in 8 days and B can do it in 10 days separately. How many days would it take for both A and B to finish the same work together?
Option 1: $\frac{33}{8}$
Option 2: $\frac{40}{9}$
Option 3: $\frac{41}{10}$
Option 4: $\frac{42}{11}$
Correct Answer: $\frac{40}{9}$
Solution :
Given:
A can do a piece of work in 8 days and B can do it in 10 days separately.
So, in 1 day A and B alone can do $\frac{1}{8}$ part and $\frac{1}{10}$ part of the work, respectively.
Now, together in 1 day they can do ($\frac{1}{8}$ + $\frac{1}{10}$) = $\frac{5 + 4}{40}$ = $\frac{9}{40}$ part of the work.
Therefore, A and B together can finish the work in (1 ÷ $\frac{9}{40}$) = $\frac{40}{9}$ days.
Hence, the correct answer is $\frac{40}{9}$.
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