Question

When the price of the chair was reduced by 15%, the number of chairs sold increased by 60%, what was the effect on the sales rupees ?\[\]
A.48%\[\]
B.36%\[\]
C.54%\[\]
D.55%\[\]

Answer 1

Hint: We denote the price of chair and number of chairs sold before the change in price as $X, Y$ and after the change as ${{X}_{n}},{{Y}_{n}}$. We find the total sales price as before the change as $SP=XY$ and after the change as $S{{P}_{n}}={{X}_{n}}{{Y}_{n}}$. We find the percentage change in total sales price at $P=\dfrac{S{{P}_{n}}-SP}{SP}\times 100$.

Complete step-by-step solution
We know that percentage is derived from the word per centum in Latin which means per hindered. The percentage in mathematics is a number or ratio expressed as a fraction of 100. We know that when we say $p%$ it means there is $p$ number of items out of every 100 items. When we say $p \%$ of $a$ it means there are $\dfrac{p}{a}\times 100$ number of items.\[\]
Let us assume the price of one chair as $X$ and the number of chairs to be sold is $Y$. The total selling price of all chairs at this point is
\[SP=Y\times X=XY\]
We are given the question that the price of the chair was reduced by 15%. The decrease in price $\Delta X$ of in one chair is 15% of $X$ which is
\[\Delta X=\dfrac{15}{100}\times X=0.15X\]
The new price of one chair ${{X}_{n}}$ after reduction in price is the,
\[{{X}_{n}}=X-\Delta X=X-.15X=0.85X\]
We are given the question that the number of chairs sold increased by 60% after the reduction in price per chair. So the increase $\Delta Y$ in the number of chairs sold is 60% of Y which is,,
\[\Delta Y=\dfrac{60}{100}\times Y=0.6Y\]
So the new number of chair sold ${{Y}_{n}}$ is
\[{{Y}_{n}}=Y+\Delta Y=Y+0.6Y=1.6Y\]
So the total selling price for all the chairs sold after reduction in price per chair is
\[S{{P}_{n}}={{X}_{n}}{{Y}_{n}}=0.85X\times 1.6Y=1.36XY\]
So the percentage change $P$ in selling price
\[P=\dfrac{S{{P}_{n}}-SP}{SP}\times 100=\dfrac{1.36XY-XY}{XY}\times 100=.36\times 100=36\% \]
So the sales price has increased by 36% and hence the correct option is B. \[\]

Note: We note that decrease in price of merchandise is also called discount which is the difference between list price and selling price and it is different from the given problem. If the price would have changed successively by $x \%,y \%,z \% $ then the new price is $P\left( 1\pm \dfrac{x}{100} \right)\left( 1\pm \dfrac{y}{100} \right)\left( 1\pm \dfrac{z}{100} \right)$.