Kaushik bought a toy for Rs. 160 and sold it for Rs. 180. The rate of profit was _______%
12.5
Understanding Profit and Loss Basics
In business mathematics, profit and loss are calculated based on the cost price and the selling price of an item. The cost price (CP) is the amount for which an item is bought, and the selling price (SP) is the amount for which it is sold.
When the selling price is greater than the cost price, a profit is made. When the selling price is less than the cost price, a loss is incurred.
In this question, Kaushik bought a toy for Rs. 160 (Cost Price) and sold it for Rs. 180 (Selling Price).
Step-by-Step Profit Calculation
First, we need to calculate the amount of profit Kaushik made. The profit is the difference between the selling price and the cost price.
The formula to calculate profit is:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} \]Using the values given in the question:
\[ \text{Profit} = 180 - 160 \] \[ \text{Profit} = 20 \]So, Kaushik made a profit of Rs. 20 by selling the toy.
Determining the Rate of Profit Percentage
The question asks for the rate of profit as a percentage. The profit percentage is calculated based on the cost price. It tells us how much profit was made relative to the original cost, expressed as a percentage.
The formula to calculate the rate of profit percentage is:
\[ \text{Rate of Profit} (\%) = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]Now, we substitute the profit amount (Rs. 20) and the cost price (Rs. 160) into the formula:
\[ \text{Rate of Profit} (\%) = \left( \frac{20}{160} \right) \times 100 \]We can simplify the fraction \(\frac{20}{160}\):
\[ \frac{20}{160} = \frac{2}{16} = \frac{1}{8} \]Now, substitute the simplified fraction back into the formula:
\[ \text{Rate of Profit} (\%) = \frac{1}{8} \times 100 \] \[ \text{Rate of Profit} (\%) = \frac{100}{8} \]Dividing 100 by 8:
\[ \frac{100}{8} = \frac{50}{4} = \frac{25}{2} = 12.5 \]So, the rate of profit was 12.5%.
Summary of Profit Rate Calculation
Here is a summary of the values and the calculated profit rate:
| Description | Amount (Rs.) |
|---|---|
| Cost Price (CP) | 160 |
| Selling Price (SP) | 180 |
| Profit (SP - CP) | \(180 - 160 = 20\) |
| Rate of Profit % | \( \left( \frac{20}{160} \right) \times 100 = 12.5\% \) |
The rate of profit was 12.5%.
Revision Table: Key Profit & Loss Formulas
Understanding these formulas is essential for solving profit and loss problems:
| Calculation | Formula |
|---|---|
| Profit | \(\text{SP} - \text{CP}\) (when SP > CP) |
| Loss | \(\text{CP} - \text{SP}\) (when CP > SP) |
| Profit Percentage (%) | \( \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \) |
| Loss Percentage (%) | \( \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100 \) |
Additional Information on Profit Calculation
Here are some extra points related to profit and loss percentage calculations:
- The profit or loss percentage is almost always calculated on the cost price unless otherwise specified.
- A profit percentage of 12.5% means that the profit earned is 12.5% of the original cost of the item.
- Problems might sometimes ask for calculations based on the selling price (e.g., profit margin), but the rate of profit typically refers to the percentage of the cost price.
- Understanding these basic concepts is crucial for tackling more complex problems involving multiple transactions or discounts.
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Important Questions from Successive Selling
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- The selling price of 24 articles is equal to the cost price of 26 articles. If, due to a change in market conditions, the selling price of each article decreases by $10\%$ and the cost price of each article increases by $5\%$, what will be the new gain or loss percentage (correct to two decimal places)?
X sells goods to Y at a profit of 20 percent and Y sells the same goods to Z at a profit of 50 percent. If the cost price for Z is Rs 9000, then what is the cost of the goods for X?
