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# TOMATO Objective 01 | ISI Entrance Exam Problem

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 $20$ %Â cut in wages. He regains his original pay by obtaining a rise of

(A) $20$ %

(B) $22 \frac{1}{2}$Â %

(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.Â $x =$Â  Rs. $80$ % of Â xÂ  = Rs.Â $\frac{4x}{5}$

and, decrease in payÂ  $= 20$ % of Rs. xÂ = $\frac{x}{5}$

Therefore, to regain the original pay, there must be a 20 % increase in the new pay and this increase has to beÂ done WITH RESPECT TO THE NEW PAYÂ as in this case, the new pay obtained in the precious case ( which isÂ $\frac{4x}{5}$ ) becomes theÂ ORIGINAL PAYÂ 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 % Â = 25 %

Therefore, option (C) is the correct option.

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## By Dr. Ashani Dasgupta

Ph.D. in Mathematics, University of Wisconsin, Milwaukee, United States.

Research Interest: Geometric Group Theory, Relatively Hyperbolic Groups.

Founder, Cheenta

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