$P$ can do a work in $25$ days and $Q$ in $20$ days. They work alternately starting with $P$. The work will…
$P$ can do a work in $25$ days and $Q$ in $20$ days. They work alternately starting with $P$. The work will be completed in:
$22$ days
$22\dfrac{1}{4}$ days
$22\dfrac{1}{2}$ days
$23$ days
Solution
In $2$ days they do $\dfrac{1}{25} + \dfrac{1}{20} = \dfrac{4 + 5}{100} = \dfrac{9}{100}$. In $11$ pairs ($22$ days) they do $\dfrac{99}{100}$. Remaining $\dfrac{1}{100}$ done by $P$ on day $23$ in $\dfrac{1/100}{1/25} = \dfrac{1}{4}$ day. Total $= 22 + \dfrac{1}{4} = 22\dfrac{1}{4}$ days.