Akash Singha Roy

Problem:

A worker suffers a \(20 \) % cut in wages. He regains his original pay by obtaining a rise of

(A) \(20 \) %

(B) \(22 \frac{1}{2}\) %

(C) \(25 \) %

(D) \(27\frac{1}{2}\) %

Solution:

Let the original pay be Rs. \(x \) (freedom of choice of unit) .

Then, new pay \(= (100 – 20) \) % of Rs. \(x = \) Rs. \(80 \) % of x = Rs. \( \frac{4x}{5}\)

and, decrease in pay \(= 20 \) % of Rs. x = \(\frac{x}{5}\)

Therefore, to regain the original pay, there must be a 20 % increase in the new pay and this increase has to be done WITH RESPECT TO THE NEW PAY* *as in this case, the new pay obtained in the precious case ( which is \(\frac{4x}{5}\) ) becomes the ORIGINAL PAY* *for the tabulation of the new pay in the second case (when the pay is again increased).

This implies that the required increase in pay must be \({\frac{x}{5}}{\frac{4x}{5}}\) times 100 % = 25 %

Therefore, option (C) is the correct option.

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