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 ( 3 )
Related Questions on Percentage
A. $$\frac{1}{4}$$
B. $$\frac{1}{3}$$
C. $$\frac{1}{2}$$
D. $$\frac{2}{3}$$
Let 100 be the base price...and we would increase 30% of this and then decrease 30% of this.
So, 100>>>130>>>91
Here the change is (100-91)=9
Which is always X^2/100 percent
Here, (30)^2/100 percent.
So the relation will always be X^2/100 percent.
Here in the math we can say that
2500*(X^2/100 )=100
So X^2=4,
So the loss is 4%.
Back calculating it from 2500>>2400>>2304.
So 2500 is the right ans.
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??