Question : A can do a piece of work in 12 days and B can do the same work in 15 days. If both do the work together, then in how many days will the work be completed?
Option 1: $7 \frac{2}{3}$
Option 2: $6 \frac{2}{3}$
Option 3: $5 \frac{2}{3}$
Option 4: $8 \frac{2}{3}$
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Correct Answer: $6 \frac{2}{3}$
Solution :
Given, A can do a piece of work in 12 days and B can do the same work in 15 days.
Let the total work be 1 unit.
Amount of work done by A in 1 day = $\frac{1}{12}$
Amount of work done by B in 1 day = $\frac{1}{15}$
Amount of work done by A and B together in 1 day = $\frac{1}{12}+\frac{1}{15}=\frac{3}{20}$
So, time taken by them to complete the whole work = $\frac{20}{3}$ = $6\frac{2}{3}$ days
Hence, the correct answer is $6\frac{2}{3}$.
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