Question

A shopkeeper increases the price of an article by X$\%$ and then decreases it by X$\%$ As a result the price of the article is reduced by $\$$180. After one more such change the price is further reduced by $\$$153. Find the original price of the article.

• A. 1200$\$$
• B. 1100$\$$
• C. 1400$\$$
• D. 1000$\$$

Answer 1

The correct option is A 1200$\$$

Let the original price be P
New price, P' = P $(1+\frac{x}{100})(1-\frac{x}{100})=P(1-\frac{x^2}{{100}^2})$
Given P - P' = 180 ------- (1)
Similarly, P" = $(1+\frac{x}{100})(1-\frac{x}{100})=P^{\prime }(1-\frac{x^2}{{100}^2})$
P' - P" = 153 -------- (2)
From (1) and (2), P' = $\frac{17}{20}$ P
Replace this in (1), P - P' = 180
P - $\frac{17}{20}P=180$
$\Rightarrow$ P = 1200$\$$