A and B together can complete a work in 24 days. B alone does 1/3rd part of this work in 12 days. How many days will A alone take to complete the remaining work?
48
Let the total work be denoted by W.
A and B together complete the work in 24 days. Therefore, their combined work rate is \(W/24\) per day.
B alone completes \(1/3\) of the work in 12 days. This means B's work rate is \(\frac{1/3 W}{12} = \frac{W}{36}\) per day.
Since the combined work rate is the sum of individual work rates, we can find A's work rate:
A's work rate + B's work rate = Combined work rate
A's work rate + \(\frac{W}{36}\) = \(\frac{W}{24}\)
A's work rate = \(\frac{W}{24} - \frac{W}{36} = \frac{3W - 2W}{72} = \frac{W}{72}\) per day.
B completes \(\frac{1}{3}\) of the work, leaving \(\frac{2}{3}\) of the work for A to complete.
The time taken by A to complete the remaining work is:
Time = \(\frac{\text{Remaining Work}}{\text{A's work rate}} = \frac{\frac{2}{3}W}{\frac{W}{72}} = \frac{2}{3} \times 72 = 48\) days.
Therefore, A alone will take 48 days to complete the remaining work.
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