Question

The owner of an art shop raises prices by X%, then later reduces all new prices by X%. After one such cycle, price decreased by Rs. 441. After a second such cycle, painting sold for Rs. 1,944.81. What was the original price?

• A. Rs. 2,756.25
• B. Rs. 2,256.25
• C. Rs. 2,500
• D. Rs. 2,000

Hint:

Price changes up then down by same percentage result in net loss proportional to square of the rate.

Answer 1

The Correct Option is A

Let original price = $P$, multiplier for one up-down cycle = $(1+\frac{x}{100})(1-\frac{x}{100}) = 1 - \frac{x^2}{10000}$. After 1 cycle: $P(1 - \frac{x^2}{10000}) = P - 441 \Rightarrow \frac{x^2}{10000} P = 441$. After 2 cycles: $P(1 - \frac{x^2}{10000})^2 = 1944.81$. Substituting $P$ from first equation and solving gives $P = 2756.25$.