Price of an item increased from रु. 16.50 to रु. 41.25. Find the percentage increase in the price.

Answer

To find the percentage increase in the price of an item that increased from रु. 16.50 to रु. 41.25, follow these steps:

### Step 1: Calculate the Increase in Price
To find the increase in price, subtract the original price from the new price.

\[ \text{Increase in Price} = \text{New Price} - \text{Original Price} \]
\[ \text{Increase in Price} = 41.25 - 16.50 \]

Calculating this gives:
\[ 41.25 - 16.50 = 24.75 \]

### Step 2: Calculate the Percentage Increase
To find the percentage increase, use the formula:

\[ \text{Percentage Increase} = \left( \frac{\text{Increase in Price}}{\text{Original Price}} \right) \times 100 \]

Substituting the values we have:

\[ \text{Percentage Increase} = \left( \frac{24.75}{16.50} \right) \times 100 \]

### Step 3: Simplify the Fraction
To simplify \(\frac{24.75}{16.50}\), we can eliminate the decimals by multiplying both the numerator and the denominator by 100:

\[ \frac{24.75 \times 100}{16.50 \times 100} = \frac{2475}{1650} \]

### Step 4: Reduce the Fraction
Now we can simplify \(\frac{2475}{1650}\) by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 2475 and 1650 is 25.

\[ \frac{2475 \div 25}{1650 \div 25} = \frac{99}{66} \]

### Step 5: Calculate the Percentage
Now, we can calculate the percentage:

\[ \text{Percentage Increase} = \frac{99}{66} \times 100 \]

Calculating this gives:

\[ \frac{99}{66} = 1.5 \]
\[ 1.5 \times 100 = 150\% \]

### Final Result
The percentage increase in the price is **150%**.

---