A does 20% less work than B. If A can finish a piece of work in 7(1/2) hours then B can finish it in A. 5 hours B. 5 (1/2) hours

Question

A does 20% less work than B. If A can finish a piece of work in 7(1/2) hours then B can finish it in 

A. 5 hours

B. \(5\frac{1}{2}\) hours

C. 6 hours

D. \(6\frac{1}{2}\) hours

Answer 1

Number of hours taken by A to finish the work = \(7\frac{1}{2}\) hours = \(\frac{15}{2}\) hours

Work done by A in one hour : \(\frac{2}{15}\)

Let number of hours taken by B to finish the work : \(\frac{1}{x}\)

A can work 20% less than B that is \(\frac{20}{100}=\frac{4}{5}\) times of B’s work.

Here , \(\frac{4}{5}:1=\frac{2}{15}:\frac{1}{x}\)

\(\frac{4}{5}=\frac{2x}{15}\)

x = \(\frac{15\,\times\,4}{5\,\times\,2}\) = 6 hours.