A alone can complete a work in 16 days and B alone in 12 days. Starting with A, they work on alternate days. The total work will be completed in
A alone can complete a work in 16 days and B alone in 12 days. Starting with A, they work on alternate days. The total work will be completed in
A12 days
B13 days
C13 $\frac{5}{7}$ days
D13 $\frac{3}{4}$ days
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Correct ansswer is: \(13 \frac{3}{4} \text{ days}\)
Explanation:
A's rate of work \(= \frac{1}{16}\)
B's rate of work = \(=\frac{1}{12}\)
In 2 days, A and B complete \(\frac{1}{16} + \frac{1}{12} \)\(=\frac{ (3+4)}{48}\) \(= \frac{7}{48}\) of the work
In \(6\times2 = 12\) days, they complete \(\frac{(7\times6)}{48}\) \(= \frac{42}{48}\) of the work
In 13 days, they complete \(\frac{42}{48} + \frac{1}{16} = \frac{45}{48}\) of the work
Remaining work \(= \frac{3}{48}\)
B can do \(\frac{1}{12} = \frac{4}{48}\)
So it takes \(13 \frac{3}{4}\)or 13.75 days to complete.
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