Renu earns a profit of 18% on selling an item for Rs. 1416/-. What is the cost price of the item?

Options

A. Rs 1,200/-
B. Rs.1.240/-
C. Rs.1,100/-
D. Rs. 1, 140/-

Answer

To find the cost price (CP) of the item when Renu earns a profit of 18% by selling it for Rs. 1416, we can follow these steps:

### Step 1: Understand the relationship between Selling Price (SP), Cost Price (CP), and Profit
The formula to calculate the Selling Price when profit is involved is:
\[ \text{SP} = \text{CP} + \text{Profit} \]
Where:
- SP = Selling Price
- CP = Cost Price
- Profit = (Profit Percentage / 100) × CP

### Step 2: Express Selling Price in terms of Cost Price
Since Renu makes a profit of 18%, we can express the Selling Price as:
\[ \text{SP} = \text{CP} + 0.18 \times \text{CP} \]
This can be simplified to:
\[ \text{SP} = \text{CP} \times (1 + 0.18) \]
\[ \text{SP} = \text{CP} \times 1.18 \]

### Step 3: Substitute the Selling Price
We know the Selling Price (SP) is Rs. 1416. So we can set up the equation:
\[ 1416 = \text{CP} \times 1.18 \]

### Step 4: Solve for Cost Price
To find the Cost Price (CP), we can rearrange the equation:
\[ \text{CP} = \frac{1416}{1.18} \]

Now, let's calculate it:
\[ \text{CP} = \frac{1416}{1.18} \approx 1200 \]

### Step 5: Conclusion
Thus, the cost price of the item is Rs. 1200.

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