A can do a piece of work in $x$ days and B can do the same work in $x + 16$ days. If both working together can do it in 15 days, find the value of $x$ .

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Solution

The correct option is C
24

Given: A can do a piece of work in $x$ days and B in $x + 16$ days.
Work done by A in one day = $\frac{1}{x}$
Work done by B in one day = $\frac{1}{x + 16}$
Work done by A and B together in one day = $\frac{1}{15}$
$\Rightarrow$ $\frac{1}{x}$ + $\frac{1}{x + 16}$ = $\frac{1}{15}$
$\Rightarrow$ $\frac{2 x + 16}{x (x + 16)} = \frac{1}{15}$
$\Rightarrow$ $x^{2} + 16 x = 15 (2 x + 16)$
$\Rightarrow$ $x^{2} - 14 x - 240 = 0$
$\Rightarrow$ $x^{2} - 24 x + 10 x - 240 = 0$
$\Rightarrow$ $x (x - 24) + 10 (x - 24) = 0$
$\Rightarrow$ $(x - 24) (x + 10) = 0$
$\Rightarrow$ $x = 24 o r x = - 10$
$\Rightarrow$ $x = 24$ as $x$ cannot be negative.

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