Question

The price of an heirloom cabbage is decreased by \[10\% \]from its original price. Sometime later, the price is then increased by \[10\% \]from its reduced price. What is the ratio of the final price to the original price?
$
  {\text{A}}{\text{. 0}}{\text{.99}} \\
  {\text{B}}{\text{. 1}} \\
  {\text{C}}{\text{. 0}}{\text{.90}} \\
  {\text{D}}{\text{. 0}}{\text{.95}} \\
 $

Answer 1

Hint: If the selling price of the product is greater than the cost price of the product, then the difference in the prices can be termed as the profit or the gain on the product while at the same time if the selling price is less than the cost price of the product, then the difference in the price is known as the loss on the product. Profit percent or, loss percent of a product is always calculated on the cost price of the product.
In this question, the price of the product is first decreased and then, increased from the new price. So, we will be finding the decreased price first, and then find the final price. Lastly we have to find the ratio.

Complete step-by-step solution
The price of an heirloom cabbage has decreased by 10% from its original price. Sometime later, the price is then increased by 10% from its reduced price.
Here, let the original price be\[x\].
Now, the decreased price =original price-10% of the original price which comes as:
\[
  {P_1} = x - \dfrac{{10}}{{100}}(x) \\
   = x - 0.1x \\
   = 0.9x - - - - (i) \\
 \]
Then, the decreased price has been increased by 10%.
So, the increased price=decreased price+ 10% of decreased price we get,
\[
  {P_2} = 0.9x + \dfrac{{10}}{{100}}\left( {0.9x} \right) \\
   = 0.9x + 0.09x \\
   = 0.99x - - - - (ii) \\
 \]
So, the final price is\[0.99x\]
The required ratio of final and original price is
\[
  P = \dfrac{{{P_2}}}{{{P_1}}} \\
   = \dfrac{{0.99x}}{x} \\
   = 0.99 \\
 \]
Hence, the ratio of the final price to the original price is 0.99

Thus Option A is the correct answer.

Note:In these types of questions, it is to be always remembered that 10% decrease followed by 10% increase does not take the price back to its original price.