Question

If a worker receives a $20$ percent cut in wages, he may regain his original pay exactly by obtaining a raise of:

• A. $20$ per cent
• B. $25$ per cent
• C. $22\frac{1}{2}$ per cent
• D. $Rs.20$

Answer 1

The correct option is B $25$ per cent

Let the wage of the worker be Rs a.

Wage after cut = $a-\frac{20a}{100}=\frac{4a}{5}$

Let m be the % raise to regain original pay.

$\frac{4a}{5}+\frac{4a}{5}\times \frac{m}{100}=a$

$\Rightarrow \frac{4a}{5}\times (1+\frac{m}{100})=a$

$\Rightarrow 1+\frac{m}{100}=\frac{5}{4}$

$\Rightarrow \frac{m}{100}=\frac{1}{4}$

$\therefore m=25\%$