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
B
12
C
10
D
9

Solution

## The correct option is C 10Let B take x hours to complete a work Then A shall take (x + 5) hours to complete the same workB'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 = 10Mathematics

Suggest Corrections

0

Similar questions
View More