A profit of 10% is made after giving a discount of 5% in a T.V. If the marked price of the TV is 2640-00, the cost price of the TV was—

Options

A. 2396
B. 2280
C. 2296
D. 2380

Answer

To find the cost price of the TV, we can follow these steps:

### Step 1: Calculate the Selling Price (SP)
The marked price (MP) of the TV is given as ₹2640. Since a discount of 5% is given, we first need to calculate the selling price after the discount.

\[ \text{Discount} = \text{MP} \times \frac{5}{100} = 2640 \times 0.05 = 132 \]

Now, we subtract the discount from the marked price to find the selling price:

\[ \text{Selling Price (SP)} = \text{MP} - \text{Discount} = 2640 - 132 = 2508 \]

### Step 2: Relate Selling Price to Cost Price
We know that a profit of 10% is made on the cost price (CP). This means that the selling price can also be expressed in terms of the cost price:

\[ \text{SP} = \text{CP} + \text{Profit} \]

Since the profit is 10% of the cost price, we can write:

\[ \text{Profit} = \text{CP} \times \frac{10}{100} = 0.1 \times \text{CP} \]

Thus, we can express the selling price as:

\[ \text{SP} = \text{CP} + 0.1 \times \text{CP} = 1.1 \times \text{CP} \]

### Step 3: Substitute the Selling Price
Now we can substitute the selling price we calculated in Step 1 into this equation:

\[ 2508 = 1.1 \times \text{CP} \]

### Step 4: Solve for Cost Price (CP)
To find the cost price, we rearrange the equation:

\[ \text{CP} = \frac{2508}{1.1} \]

Calculating this gives:

\[ \text{CP} = 2280 \]

### Conclusion
The cost price of the TV was ₹2280.

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