If selling price is Rs 840 and profit is 5%, then what is the cost price?

Options

A. 750
B. 800
C. 810
D. 900

Answer

To find the cost price when the selling price is Rs 840 and the profit is 5%, we can follow these steps:

### Step 1: Understand the relationship between Selling Price (SP), Cost Price (CP), and Profit
The relationship can be expressed as:
\[ \text{SP} = \text{CP} + \text{Profit} \]
Since profit is a percentage of the cost price, we can also express it as:
\[ \text{Profit} = \frac{\text{Profit Percentage}}{100} \times \text{CP} \]

### Step 2: Express Selling Price in terms of Cost Price
Given that the profit is 5%, we can express the selling price as:
\[ \text{SP} = \text{CP} + \frac{5}{100} \times \text{CP} \]
This simplifies to:
\[ \text{SP} = \text{CP} \left(1 + \frac{5}{100}\right) = \text{CP} \times \frac{105}{100} \]

### Step 3: Substitute the Selling Price
Now, we know the selling price (SP) is Rs 840. Therefore, we can write:
\[ 840 = \text{CP} \times \frac{105}{100} \]

### Step 4: Solve for Cost Price (CP)
To find the cost price, we rearrange the equation:
\[ \text{CP} = 840 \times \frac{100}{105} \]

### Step 5: Calculate the Cost Price
Now, we can calculate:
\[ \text{CP} = 840 \times \frac{100}{105} = 840 \div 1.05 \]
Calculating this gives:
\[ \text{CP} = 800 \]

### Final Answer
Thus, the cost price is Rs 800.

---