Price of 1 kg of rice is increased by 50 percent and the old price of the rice is Rs. 60. What is the new price of the rice per kg?
Rs. 90
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
- Identify the old price of the rice.
- Identify the percentage increase.
- Calculate the amount of the increase. This is the percentage increase applied to the old price.
- 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
| Detail | Value |
|---|---|
| Old Price | Rs. 60 |
| Percentage Increase | 50% |
| Increase Amount (50% of 60) | Rs. 30 |
| New Price (Old Price + Increase) | Rs. 90 |
Revision Table: Key Terms in Price Increase
| Term | Definition | How it relates to the problem |
|---|---|---|
| Old Price (Original Price) | The price before any change occurred. | Rs. 60 is the old price of rice. |
| Percentage Increase | The relative amount by which a value increases, expressed as a percentage of the original value. | The price increased by 50%. |
| Increase Amount | The absolute value that is added to the original price due to the percentage increase. | Calculated as 50% of Rs. 60, which is Rs. 30. |
| New Price | The final price after the increase has been applied. | Old Price + Increase Amount = Rs. 60 + Rs. 30 = Rs. 90. |
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.
Important Questions from Percentage
Radha saves 25% of her income. If her expenditure increases by 20% and her income increases by 29%, then her savings increase by;
The income of A is 45% more than the income of B and the income of C is 60% less than the sum of the incomes of A and B. The income of D is 20% more than that of C. If the difference between the incomes of B and D is Rs. 13200, then the income (in Rs.) of C is:
The price of cooking oil increased by 25%. Find by how much percentage a family must reduce its consumption in order to maintain the same budget.
The population of a city increased by 30% in the first year and decreased by 15% in the next year. If the present population is 11,050 then population 2 years ago was:
The income of A is 30% less than the income of B and the income of B is 137.5% more than that of C. If the income of A is Rs. 28500 less than that of B, then the income (in Rs.) of C is:
