The price of a watch increases every year by 25%. If the present price is Rs 7500, then what was the price (in Rs) 2 years ago?

Options

A. A)4800
B. B)5200
C. C)6200
D. D)3600

Answer

To find the price of the watch 2 years ago, we can use the concept of reverse percentage increase. The watch's price increases by 25% each year, which means that the price after one year can be calculated as:

\[ \text{New Price} = \text{Old Price} + 25\% \text{ of Old Price} \]
or
\[ \text{New Price} = \text{Old Price} \times \left(1 + \frac{25}{100}\right) = \text{Old Price} \times \frac{5}{4} \]

Let the price of the watch 2 years ago be \( K \). After one year, the price will be:

\[ \text{Price after 1 year} = K \times \frac{5}{4} \]

After the second year, the price will be:

\[ \text{Price after 2 years} = \left(K \times \frac{5}{4}\right) \times \frac{5}{4} = K \times \left(\frac{5}{4}\right)^2 \]

Since we know the current price is Rs. 7500, we can set up the equation:

\[ K \times \left(\frac{5}{4}\right)^2 = 7500 \]

Now we can simplify this equation step by step.

### Step 1: Calculate \(\left(\frac{5}{4}\right)^2\)

\[ \left(\frac{5}{4}\right)^2 = \frac{25}{16} \]

### Step 2: Substitute back into the equation

\[ K \times \frac{25}{16} = 7500 \]

### Step 3: Solve for \( K \)

To isolate \( K \), multiply both sides by \(\frac{16}{25}\):

\[ K = 7500 \times \frac{16}{25} \]

### Step 4: Calculate \( 7500 \times \frac{16}{25} \)

First, simplify \( 7500 \div 25 \):

\[ 7500 \div 25 = 300 \]

Now multiply by 16:

\[ K = 300 \times 16 = 4800 \]

### Conclusion

The price of the watch 2 years ago was Rs. 4800.

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