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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
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B
25 per cent
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C
2212 per cent
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D
Rs.20
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Solution

The correct option is B $$25$$ per cent
Let the wage of the worker be Rs a.
Wage after cut = $$a- \cfrac{20a}{100}= \cfrac{4a}{5}$$
Let m be the % raise to regain original pay.
$$\cfrac { 4a }{ 5 } +\cfrac { 4a }{ 5 } \times \cfrac { m }{ 100 } =a$$
$$\Rightarrow \dfrac{4a}{5}\times (1+\dfrac{m}{100}) = a$$
$$\Rightarrow 1+\dfrac{m}{100} = \dfrac{5}{4}$$
$$\Rightarrow \dfrac{m}{100} = \dfrac{1}{4}$$
$$ \therefore m=25\%$$

Mathematics

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