Question

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.$1944.811$. What was the original price of the painting (in Rs)?

• A. $2756.25$
• B. $2256.25$
• C. $2500$
• D. $2000$

Answer 1

The correct option is A $2756.25$

$\Rightarrow$ Let the original price be $P$ and $X\%=a$

$\Rightarrow$ $P-P\times (1+a)(1-a)=441$

$\Rightarrow$ $P\times a^2=441$ ---- ( 1 )

$\Rightarrow$ Again, $P\times \left[\right(1+a\left)\right(1-a){]}^2=1944.81$

$\Rightarrow$ $P\times (1-a^2{)}^2=1944.81$ ----- ( 2 )

Dividing ( 2 ) by ( 1 ). we get,

$\Rightarrow$ $\frac{P\times (1-a^2{)}^2}{P\times \left(a^2\right)}=\frac{1944.81}{441}$

$\Rightarrow$ $\frac{(1-a^2{)}^2}{a^2}=4.41$

$\Rightarrow$ $\frac{1-a^2}{a}=2.1$ [Taking square root on both sides]

$\therefore$ $a=\frac{2}{5}$

$\Rightarrow$ $P\times (\frac{2}{5}{)}^2=441$ [Substituting value in ( 1 )]

$\Rightarrow$ $P=\frac{441\times 25}{4}=Rs.2756.25$