The price of a bike is increased by 25%, by how much percent, must the new price of this bike be decreased to restore its original price?
Correct Answer: Option B
Suppose that the original price of the bike = x Rs. Then new price of the bike
\(= x + x \times \frac{{25}}{{100}} = \frac{5}{4}x{\rm{ }}\)
To restore the original price, the new price must be decreased by
\(\frac{5}{4}x - x = \frac{x}{4}\)
So required percentage \(= \frac{{\frac{x}{4}}}{{\frac{5}{4}x}} \times 100\%\)
= 20%
Alternate method (short trick):
When price of an article is increased by x%, then required reduction in the price of the article to restore the original price would be
\(\left( {\frac{r}{{100 + r}} \times 100} \right)\%\)
Hence, required percentage \(= \frac{{25}}{{125}} \times 100\% = 20\%\)
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