$A$ and $B$ working separately can do a piece of work in 10 and 15 days respectively. If they work on alternate days beginning with $A$ , in how many days will the work be completed?

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Solution

Work done by $A$ in 1 day $= \frac{1}{10}$
Work done by $B$ in 1 day $= \frac{1}{15}$
Work done by $A$ and $B$ in 2 days $= \frac{1}{10} + \frac{1}{15} = \frac{3 + 2}{30} = \frac{5}{30} = \frac{1}{6}$
$∵ \frac{1}{6}$ work is done in 2 days
1 work will be done in $2 \times 6 = 12$ days.

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A and B working separately can do a piece of work in 10 and 15 days respectively. If they work on alternate days beginning with A, in how many days will the work be completed?

Work done by A in 1 day =110Work done by B in 1 day =115Work done by A and B in 2 days =110+115=3+230=530=16∵16 work is done in 2 days1 work will be done in 2×6=12 days.

$A$ and $B$ working separately can do a piece of work in 10 and 15 days respectively. If they work on alternate days beginning with $A$ , in how many days will the work be completed?

Work done by $A$ in 1 day $= \frac{1}{10}$
Work done by $B$ in 1 day $= \frac{1}{15}$
Work done by $A$ and $B$ in 2 days $= \frac{1}{10} + \frac{1}{15} = \frac{3 + 2}{30} = \frac{5}{30} = \frac{1}{6}$
$∵ \frac{1}{6}$ work is done in 2 days
1 work will be done in $2 \times 6 = 12$ days.