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 that A takes to complete the work individually is 

(a) 15 

(b) 12 

(c) 10 

(d) 9

Answer 1

(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, \(\frac{1}{X}\)+ \(\frac{1}{(X+5)}\) = \(\frac{1}{6}\)

\(\Rightarrow\) \(\frac{X+5+X}{X(X+5)}\) = \(\frac{1}{6}\) \(\Rightarrow\) \(\frac{2X+5}{X^2+5X}\) = \(\frac{1}{6}\)

\(\Rightarrow\) 12x + 30 = x² + 5x

\(\Rightarrow\) x² – 7x – 30 = 0

\(\Rightarrow\) x² – 10x + 3x – 30 = 0

\(\Rightarrow\) x(x – 10) + 3(x – 10) = 0

\(\Rightarrow\) (x – 10) = 0 or (x + 3) = 0

x = 10 or – 3

Neglecting negative value x = 10.