On selling a television for Rs.8500, a person Incurs a loss of 15%. What will be the selling price of the television to gain 5%?

Options

A. Rs. 9,500
B. Rs. 10,000
C. Rs. 10,500
D. Rs. 9,000

Answer

To find the selling price of the television to gain 5%, we will follow these steps:

### Step 1: Determine the Cost Price (CP) of the Television
Given that selling the television for Rs. 8500 incurs a loss of 15%, we can express the selling price (SP) in terms of the cost price (CP).

If there is a loss of 15%, it means the selling price is 85% of the cost price. We can write this as:
\[ SP = CP \times \left(1 - \frac{Loss\%}{100}\right) \]
\[ 8500 = CP \times \left(1 - \frac{15}{100}\right) \]
\[ 8500 = CP \times 0.85 \]

### Step 2: Calculate the Cost Price (CP)
To find the cost price, we rearrange the equation:
\[ CP = \frac{8500}{0.85} \]
\[ CP = 10000 \]

### Step 3: Determine the Selling Price for a 5% Gain
To find the selling price for a 5% gain, we need to calculate 105% of the cost price (since a gain of 5% means selling at 105% of the CP).

We can express this as:
\[ SP_{gain} = CP \times \left(1 + \frac{Gain\%}{100}\right) \]
\[ SP_{gain} = 10000 \times \left(1 + \frac{5}{100}\right) \]
\[ SP_{gain} = 10000 \times 1.05 \]

### Step 4: Calculate the Selling Price (SP)
Now we can calculate the selling price:
\[ SP_{gain} = 10000 \times 1.05 = 10500 \]

### Final Answer
The selling price of the television to gain 5% is Rs. 10,500.

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