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

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}

1. Is there any short cut tricks to solve this question?

2. x2*y = 106 how is this happen
And y(1-100/y)2 = 2304
y = 2500. How is it possible??

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