Question

The price of an article was increased by $P\%$. Later the new price was decreased by $P\%$. If the latest price was $RS1$, then the original price was?

• A. $Rs.5$
• B. $Rs\frac{1-p^2}{100}$
• C. $Rs\frac{10,000}{10,000-p^2}$
• D. $Rs\sqrt{\frac{1-p^2}{100}}$

Answer 1

Answer: (C)

$Rs\frac{10,000}{10,000-p^2}$

Consider the problem

Let the original price $=Rsx$

Price after $p\%$ increase $=(100+p)\%$ of $x$

$=\frac{\left(100+p\right)x}{100}$

New price after $p\%$ decrease

$=\left(100-p\right)\%of\left[\frac{\left(100+p\right)x}{100}\right]$

$\begin{array}{c}\\ =\frac{\left(100-p\right)}{100}\times \frac{\left(100+p\right)}{100}\times x\\ =\frac{\left(100-p\right)\left(100+p\right)}{100\times 100}\times x=1\end{array}$

Or

$\begin{array}{c}x=\frac{100\times 100}{\left(100-p\right)\left(100+p\right)}\\ =\frac{10000}{10000-p^2}\end{array}$

Hence, Option $C$ is the correct answer.