A and B can do a work in \(10\) and \(15\text{ days}\) respectively. If they work on alternate days in this, A starts first. Then the work will be completed in how many days?
\(12\text{ days}\)
12 days is correct.
In alternate-day work, find the work done in one complete two-day cycle and count how many cycles are needed.
One-day work: A \(= \dfrac{1}{10}\), B \(= \dfrac{1}{15}\).
Each two-day cycle (A then B) completes \(\dfrac{1}{10} + \dfrac{1}{15} = \dfrac{3 + 2}{30} = \dfrac{1}{6}\) of the work.
The whole work needs \(6\) such cycles, i.e. \(6 \times 2 = 12\) days, ending exactly on B's day.
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Important Questions from Time and work
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