Question : Directions: The price of an article has been reduced by 25%. To restore the original price, the new price must be increased by?
Option 1: $11\frac{1}{9}\%$
Option 2: $66\frac{2}{3}\%$
Option 3: $9\frac{1}{11}\%$
Option 4: $33\frac{1}{3}\%$
Correct Answer: $33\frac{1}{3}\%$
Solution :
Let the price of an article be Rs 100.
The price of an article after reduction = 100 – 25 % of 100
The price of an article after reduction = 100 – ($\frac{25}{100}$ × 100) = 100 – 25 = Rs 75
Now, let the percentage increase in the price be x %.
So, according to the question –
⇒ 75 + x % of 75 = 100
⇒ x % of 75 = 100 – 75 = 25
⇒ $\frac{x}{100}$ × 75 = 25
⇒ x = $\frac{25 × 100}{75}$
⇒ x = $33\frac{1}{3}\%$
So, the price must be increased by $33\frac{1}{3}\%$. Hence, the fourth option is correct.
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