Question : John can do a piece of work alone in 20 days, while Ravi can do the same piece of work alone in 28 days. In how many days can the duo complete the same work if they work together?
Option 1: $11 \frac{1}{3}$
Option 2: $12 \frac{2}{3}$
Option 3: $11 \frac{2}{3}$
Option 4: $12 \frac{1}{3}$
Correct Answer: $11 \frac{2}{3}$
Solution :
John can do a piece of work alone in = 20 days
Ravi can do the same piece of work alone in = 28 days
Efficiency of John = $\frac{1}{20}$
Efficiency of Ravi = $\frac{1}{28}$
Combine efficiency = $\frac{1}{20} + \frac{1}{28} = \frac{12}{140} = \frac{3}{35}$
Now, efficiency = $\frac{\text{Total work}}{\text{Time taken}}$
Days taken by duo to complete the same work if they work together = (1 ÷ $\frac{3}{35}$) = $\frac{35}{3} $ = $11\frac{2}{3}$ days
Hence, the correct answer is $11\frac{2}{3}$.
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