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Explore the Back-StoryThis is a problem from TOMATO Objective 01 based on worker and wages. This problem is helpful for ISI Entrance Exam. Try out the problem. (By Akash Singha Roy)

**Problem: TOMATO Objective 01**

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 the 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.

This is a problem from TOMATO Objective 01 based on worker and wages. This problem is helpful for ISI Entrance Exam. Try out the problem. (By Akash Singha Roy)

**Problem: TOMATO Objective 01**

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 the 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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