Question : A alone can do a work in 16 days and B alone can do the same work in 12 days. If they worked together on it for 4 days and A left. How long did B take to finish the remaining work?
Option 1: 7 days
Option 2: 5 days
Option 3: 6 days
Option 4: 8 days
Correct Answer: 5 days
Solution :
Time taken by A to do the work = 16 days
Part of work done by A in a day = $\frac{1}{16}$
Time taken by B to do the work = 12 days
Part of work done by B in a day = $\frac{1}{12}$
Part of work done by A and B in 4 days = 4 × ( $\frac{1}{16}$+$\frac{1}{12}$) = 4 × $\frac{3+4}{48}$ = $\frac{7}{12}$
Remaining work = $1-\frac{7}{12}$ = $\frac{5}{12}$
Time taken by B to do the remaining work = $\frac{\frac{5}{12}}{\frac{1}{12}}$ = 5 days
Hence, the correct answer is 5 days.
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