The price of a T.V. set inclusive of tax of 9% is Rs 13,407. Find its marked price. If tax is increased to 13%, how much more does the customer has to pay for the T.V. set ?

Answer

To solve the problem step by step, we will break it down into two parts: finding the marked price of the TV set and calculating how much more the customer has to pay when the tax is increased from 9% to 13%.

### Step 1: Finding the Marked Price with 9% Tax

1. **Let the marked price be \( x \)**.
2. **Calculate the selling price including tax**: The selling price (SP) is given as Rs 13,407, which includes a 9% tax.
3. **Express the selling price in terms of the marked price**:
\[ SP = x + 0.09x = 1.09x \]
4. **Set up the equation**:
\[ 1.09x = 13,407 \]
5. **Solve for \( x \)**:
\[ x = \frac{13,407}{1.09} \approx 12,300 \]
Thus, the marked price of the TV set is Rs 12,300.

### Step 2: Calculating the New Selling Price with 13% Tax

1. **Now, calculate the selling price with a 13% tax**:
- The new tax is 13%, so we express the new selling price (SP2) as:
\[ SP2 = x + 0.13x = 1.13x \]
2. **Substitute the marked price**:
\[ SP2 = 1.13 \times 12,300 \]
3. **Calculate the new selling price**:
\[ SP2 = 13,899 \]
Thus, the new selling price with 13% tax is Rs 13,899.

### Step 3: Finding the Additional Amount Paid by the Customer

1. **Calculate the difference in selling prices**:
\[ \text{Difference} = SP2 - SP = 13,899 - 13,407 \]
2. **Calculate the difference**:
\[ \text{Difference} = 492 \]
Therefore, the customer has to pay an additional Rs 492 when the tax is increased from 9% to 13%.

### Final Answers:
- The marked price of the TV set is Rs 12,300.
- The customer has to pay an additional Rs 492.