Calculating Price Increase: 50% Rise on Rice Price

This problem asks us to find the new price of 1 kg of rice after a 50 percent increase from its original price of Rs. 60. This is a straightforward percentage increase calculation.

Understanding Percentage Increase

A percentage increase means that a certain percentage of the original value is added to the original value. In this case, the price of rice is increasing by 50% of its old price.

Step-by-Step Solution to Find the New Rice Price

1. Identify the old price of the rice.
2. Identify the percentage increase.
3. Calculate the amount of the increase. This is the percentage increase applied to the old price.
4. Add the increase amount to the old price to find the new price.

Applying the Steps to the Rice Price Problem

• Old Price: The old price of 1 kg of rice is given as Rs. 60.
• Percentage Increase: The price is increased by 50 percent.
• Calculate the Increase Amount: The increase amount is 50% of the old price (Rs. 60).

  To calculate 50% of 60, we can write the percentage as a fraction or a decimal:

  As a fraction: \( \text{Increase} = \frac{50}{100} \times 60 \)

  \( \text{Increase} = \frac{1}{2} \times 60 \)

  \( \text{Increase} = \text{Rs.} \; 30 \)

  As a decimal: \( \text{Increase} = 0.50 \times 60 \)

  \( \text{Increase} = \text{Rs.} \; 30 \)

  So, the price increase is Rs. 30.

• Calculate the New Price: The new price is the old price plus the increase amount.

  \( \text{New Price} = \text{Old Price} + \text{Increase Amount} \)

  \( \text{New Price} = \text{Rs.} \; 60 + \text{Rs.} \; 30 \)

  \( \text{New Price} = \text{Rs.} \; 90 \)

The new price of 1 kg of rice is Rs. 90.

Summarizing the Price Calculation

Revision Table: Key Terms in Price Increase

Additional Information: Calculating Percentage Changes

Understanding how to calculate percentage changes is useful in many real-world situations, including prices, discounts, and growth rates.

The general formula for calculating a percentage change is:

\( \text{Percentage Change} = \left( \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \right) \times 100\% \)

If the New Value > Old Value, it's a percentage increase.

If the New Value < Old Value, it's a percentage decrease.

Alternatively, to find the new value directly after a percentage increase (P%):

\( \text{New Value} = \text{Old Value} \times \left( 1 + \frac{\text{P}}{100} \right) \)

Using this formula for our rice price problem:

\( \text{New Price} = 60 \times \left( 1 + \frac{50}{100} \right) \)

\( \text{New Price} = 60 \times \left( 1 + 0.50 \right) \)

\( \text{New Price} = 60 \times 1.50 \)

\( \text{New Price} = \text{Rs.} \; 90 \)

This formula confirms our previous calculation. Multiplying by \( (1 + \frac{P}{100}) \) directly gives you the final value after a P% increase.