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CAT 2001 | Question: 35

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The owner of an art shop conducts his business in the following manner: Every once in a while he raises his prices by $\text{X}\%$, then a while later he reduces all the new prices by $\text{X}\%.$ After one such up-down cycle, the price of a painting decreased by Rs. $441.$ After a second up-down cycle the painting was sold for Rs. $1,944.81.$ What was the original price of the painting?

  1. Rs $2,756.25$
  2. Rs $2,256.25$
  3. Rs $2,500$ 
  4. Rs $2,000$

1 Answer

1 1 vote
Let the original price be P and x%=a
P-P*(1+a)*(1-a)=441
P*a^2=441
Again,
P*((1+a)*(1-a))^2=1944.81
P*(1-a^2)^2=1944.81
Dividing,
(1-a^2)^2/a^2=1944.81/441=4.41
(1-a^2)/a=2.1
a=2/5
P*(2/5)^2=441
P=441*25/4=2756.25
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