Q6 PERCENTAGES
The owner of an art shop conducts his business in the following manner: every once in a while he raises his prices by X%, then a while later he reduces all the new prices by 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?
a. Rs. 2,756.25
b. Rs. 2,256.25
c. Rs. 2,500
d. Rs. 2,000Let 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
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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