Due to new rules of TRAI, Rs. 154 is fixed as FTA upto 100 SD channels and additional Rs. 10 pe 3 HD or 6 SD channels. A person paying Rs. 400 earlier, has now subscribed for 80 SD channel pack worth Rs.250 and 9 HD channels pack at Rs. 4 per channel. What is his percent increase in bill amount?

Options

A. `32.5%`
B. `13.25%`
C. `20%`
D. `17.5%`

Answer

To solve the problem step by step, we will calculate the new bill amount and then find the percentage increase from the old bill amount to the new bill amount.

### Step 1: Identify the old bill amount
The old bill amount is given as Rs. 400.

### Step 2: Calculate the new bill amount
The new bill consists of three components:
1. **Fixed charge for FTA up to 100 SD channels**: Rs. 154
2. **Cost of the SD channel pack**: Rs. 250 for 80 SD channels
3. **Cost of the HD channels**: 9 HD channels at Rs. 4 per channel

#### a. Calculate the cost for the HD channels
Cost for 9 HD channels = 9 channels × Rs. 4/channel = Rs. 36

#### b. Calculate the additional charge for HD channels
For every 3 HD channels, there is an additional charge of Rs. 10. Since there are 9 HD channels:
- Number of groups of 3 HD channels = 9 / 3 = 3
- Additional charge = 3 × Rs. 10 = Rs. 30

#### c. Combine all components to find the total new bill
Total new bill = Fixed charge + Cost of SD channel pack + Cost of HD channels + Additional charge
= Rs. 154 + Rs. 250 + Rs. 36 + Rs. 30

Calculating this:
- Rs. 154 + Rs. 250 = Rs. 404
- Rs. 404 + Rs. 36 = Rs. 440
- Rs. 440 + Rs. 30 = Rs. 470

So, the new bill amount is Rs. 470.

### Step 3: Calculate the percentage increase in the bill amount
Percentage increase is calculated using the formula:
\[ \text{Percentage Increase} = \left( \frac{\text{New Amount} - \text{Old Amount}}{\text{Old Amount}} \right) \times 100 \]

Substituting the values:
\[ \text{Percentage Increase} = \left( \frac{470 - 400}{400} \right) \times 100 \]
\[ = \left( \frac{70}{400} \right) \times 100 \]
\[ = 0.175 \times 100 = 17.5\% \]

### Conclusion
The percentage increase in the bill amount is **17.5%**.

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