# At the beginning of a year ,the owner of a jewel shop raised the price of all the jewels in his shop by x% and lowered them by x%. The price of one jewel after this up and down cycle reduced by Rs. 100. The owner carried out the same procedure after a month. After this second up-down cycle,the price of that jewel was Rs. 2304. Find the original price of that jewel(in Rs.)

A. 2500

B. 2550

C. 2600

D. 2650

E. None of these

**Answer: Option A **

__Solution(By Examveda Team)__

$$\eqalign{
& {\text{Let}}\,{\text{the}}\,{\text{original}}\,{\text{price}} = y, \cr
& {\text{After}}\,{\text{first}}\,{\text{change,}}\,{\text{it}}\,{\text{becomes}}, \cr
& y \times \left( {1 + {\frac{x}{{100}}} } \right) \cr
& {\text{After}}\,{\text{second}}\,{\text{change,}}\,{\text{it}}\,{\text{becomes}} \cr
& y \times \left( {1 + {\frac{x}{{100}}} } \right)\left( {1 - {\frac{x}{{100}}} } \right) \cr
& = y\left( {1 - {{\left( {\frac{x}{{100}}} \right)}^2}} \right) \cr
& {\text{Thus}}, \cr
& {x^2} \times y = {10^6} - - - - \left( 1 \right) \cr
& {x^2} = \frac{{{{10}^6}}}{y} \cr
& {\text{Now}}, \cr
& y{\left( {1 - {\frac{{{{10}^6}}}{{10000y}}} } \right)^2} \cr
& = 2304\left( {{\text{similar}}\,{\text{to}}\,{\text{above}}} \right) \cr
& y{\left( {1 - \frac{{100}}{y}} \right)^2} = 2304 \cr
& y = 2500 \cr} $$ ## Join The Discussion

## Comments ( 2 )

Related Questions on Percentage

A. $$\frac{1}{4}$$

B. $$\frac{1}{3}$$

C. $$\frac{1}{2}$$

D. $$\frac{2}{3}$$

Is there any short cut tricks to solve this question?

x2*y = 106 how is this happen

And y(1-100/y)2 = 2304

y = 2500. How is it possible??