Question

The price of an heirloom cabbage is decreased by $10\%$ from its original price. Some time later, the price is then increased by $10\%$ from its reduced price. What is the ratio of the final price to the original price?

• A. $0.99$
• B. $1$
• C. $0.90$
• D. $0.95$

Answer 1

The correct option is A $0.99$

Let the original price be $100$.
When the price of heirloom cabbage is decreased by $10\%$ its price will be
$100-\frac{10}{100}\times 100$
$100-10=90$
Sometimes later the price is increased by $10\%$, so the new price will be
$90+\frac{10}{100}\times 90$
$90+9=99$
So final price is $99$.
Hence, ratio of final price to original price will be,
$\frac{99}{100}=0.99$