A takes 5 hours more time than that taken by B to complete a work. If working together they can complete a work in 6 hours, then the number of hours , then the number of hours that a takes to complete the work individually is

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Solution

The correct option is C 10
Let B take x hours to complete a work Then A shall take (x + 5) hours to complete the same work
B's 1 hours work = $\frac{1}{x}$ A's 1 hours' work = $\frac{1}{x + 5}$ Given $\frac{1}{x} + \frac{1}{(x + 5)} = \frac{1}{6}$
$\Rightarrow \frac{x + 5 + x}{x (x + 5)} = \frac{1}{6} \Rightarrow \frac{2 x + 5}{x^{2} + 5 x} = \frac{1}{6}$ $\Rightarrow 12 x + 30 = x^{2} + 5 x \Rightarrow x^{2} - 7 x - 30 = 0$
$\Rightarrow x^{2} - 10 x + 3 x - 30 = 0 \Rightarrow x (x - 10) + 3 (x - 10) = 0$
$x = 10 o r - 3$ Neglecting negative value x = 10

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