Question

A shopkeeper increases the price of a commodity by $x\%$. Sometime later, he reduces the new price by $y\%$ and notices that the price is now the same as it was originally. The value of $\frac{1}{y}-\frac{1}{x}$ is

• A. $-\frac{1}{100}$
• B. 0
• C. $\frac{1}{100}$
• D. Not uniquely determinable

Answer 1

The correct option is C $\frac{1}{100}$

Let the price of the commodity be Rs. $100$

New price after increase by $x$% = $100+x$

New price after decrease by $y$% = $(100+x)(1-\frac{y}{100})$

This price is equal to the original price

That is,

$(100+x)(1-\frac{y}{100})=100$

$(100+x)(100-y)=100\times 100$

$10000-100y+100x-xy=10000$

$100x-100y-xy=0$

$100x-100y=xy$

Dividing both sides by 100xy

$\frac{100x}{100xy}-\frac{100y}{100xy}=\frac{xy}{100xy}$

$\frac{1}{y}-\frac{1}{x}=\frac{1}{100}$