Question

A does 20% less work than B. If A can finish a piece of work in 72 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

A's 1 hour's work $=\frac{2}{15}$

A and B's ratio in work $=\frac{100-20}{100}:1$

$=\frac{80}{100}:1$

$=\frac{4}{5}:1$

Let ratio be, $\frac{4}{5}x$ and x, then

$\frac{4}{5}:1=\frac{2}{15}:\frac{1}{x}$

$1\times \frac{2}{15}=\frac{4}{5}\times \frac{1}{x}=\frac{2}{15}=\frac{4}{5x}$

$2\times 5x=4\times 15\Rightarrow x=\frac{4\times 15}{2\times 5}=6$

$\therefore$ B can finish the work in 6 hours