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Question

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 


A
15
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B
12
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C
10
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D
9
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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 = $$\displaystyle \frac{1}{x}$$ A's 1 hours' work = $$\displaystyle \frac{1}{x+5}$$ Given $$\displaystyle \frac{1}{x}+\frac {1}{(x+5)}=\frac {1}{6}$$
$$\displaystyle \Rightarrow \frac{x+5+x}{x(x+5)}=\frac{1}{6}\Rightarrow \frac{2x+5}{x^{2}+5x}=\frac{1}{6}$$ $$\displaystyle \Rightarrow 12x+30=x^{2}+5x\Rightarrow x^{2}-7x-30=0$$
$$\displaystyle \Rightarrow x^{2}-10x+3x-30=0\Rightarrow x(x-10)+3(x-10)=0$$
$$\displaystyle x=10\: \: or\: \: -3$$ Neglecting negative value x = 10

Mathematics

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