Question : Tom can do a piece of work in 7 days, whereas Jay can do the same work in 14 days. How long will it take to finish the work if both work together?
Option 1: $5 \frac{2}{3}$ days
Option 2: $4 \frac{2}{3}$ days
Option 3: $7 \frac{2}{3}$ days
Option 4: $2 \frac{2}{3}$ days
Correct Answer: $4 \frac{2}{3}$ days
Solution :
Time taken by Tom to complete the work = 7 days
Part of work done by Tom in a day = $\frac{1}{7}$
Time taken by Jay to complete the work = 14 days
Part of work done by Jay in a day = $\frac{1}{14}$
Part of the work done by Tom and Jay together in a day = $\frac{1}{7}+\frac{1}{14}=\frac{2+1}{14} = \frac{3}{14}$
Time taken by Tom and Jay together to complete the work = $\frac{14}{3} = 4\frac{2}{3}$ days
Hence, the correct answer is $4\frac{2}{3}$ days.
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