TOMATO Objective 01

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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