A can do a piece of work in 24 days while B can do it in 30 days. In how many days can they complete it, if they work together ?

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Solution

Let total works $= x$
$A$ takes $24 d a y s$ to complete $x$
$\Rightarrow$ In one day a complete work $= \frac{x}{24}$
$B$ completes $x$ works in $30 d a y s$
$\Rightarrow$ In $1$ day $B$ completes work $= \frac{x}{30}$
If $A$ and $B$ work together,
work done in one day $= \frac{x}{24} + \frac{x}{30}$
$= \frac{5 x + 4 x}{120} = \frac{9 x}{120} = \frac{3 x}{40}$
Let they take $n$ days to complete entire work.
$\Rightarrow$ Total work $= n \times \frac{3 x}{40} = x$
$\Rightarrow n = \frac{40}{3} d a y s$

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