A can do $\frac{1}{4}$ of a work in 5 days and B can do $\frac{1}{3}$ of the same work in 10 days. Find the number of days in which both working together will complete the work.

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Solution

A can do $\frac{1}{4}$ of work in = 5 days
$∴$ A can do 1 work in $= 5 \times 4$ days
= 20 days
B can do $\frac{1}{3}$ of work in = 10 days
$∴$ B can do 1 work in $= 10 \times 3$ days
= 30 days
$∴$ A's 1 day work $= \frac{1}{20}$
B's 1 day work $= \frac{1}{30}$
(A+B)'s 1 day work $= \frac{1}{20} + \frac{1}{30}$
$= \frac{3 + 2}{60}$
$= \frac{5}{60}$
$= \frac{1}{12}$
$∴$ A and B working together will complete the work in = 12 days.

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