The price of an article is increased by r%. The new price was decreased by r% later. Now the latest price is Rs. 1. What was the original price of the article?

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SSC CGL 2023 Tier-I Official Paper (Held On: 20 Jul 2023 Shift 3)
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  1. \(\rm\frac{10000}{10000−r^{2}}\)
  2. \(\rm\frac{10000−r^{2}}{10000}\)
  3. \(\rm\frac{100}{100−r^{2}}\)
  4. \(\rm\frac{100}{1−r^{2}}\)

Answer (Detailed Solution Below)

Option 1 : \(\rm\frac{10000}{10000−r^{2}}\)
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Detailed Solution

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Given:

The price of an article is increased by r%.

The new price was decreased by r% later.

Now the latest price is Rs. 1.

Concept used:

If  the price of an article is increased by r% and then decreased by r% , the total decrease is r2/100

Calculation:

Let the old price be Rs x

As per the question,

   \(x - \frac{r^2}{100} \times \frac{x}{100}\)  = 1

⇒ x = \(\rm\frac{10000}{10000−r^{2}}\)

∴ The correct option is 1

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