The price of an article inclusive of 12% tax is Rs 2016. Find its marked price. If the tax is reduced to 7% , how much less will the customer pay for the article.

Answer

To solve the problem step by step, we will break it down into parts.

### Step 1: Understand the Given Information
The price of an article inclusive of a 12% tax is Rs 2016. We need to find the marked price (which is the price before tax) and then determine how much less a customer will pay if the tax is reduced to 7%.

### Step 2: Set Up the Equation for Marked Price
Let the marked price be \( X \). The price inclusive of tax can be expressed as:
\[ X + 12\% \text{ of } X = 2016 \]
This can be rewritten as:
\[ X + \frac{12}{100}X = 2016 \]
Combining the terms gives:
\[ X \left(1 + \frac{12}{100}\right) = 2016 \]
\[ X \left(\frac{112}{100}\right) = 2016 \]

### Step 3: Solve for Marked Price \( X \)
To find \( X \), we can rearrange the equation:
\[ X = \frac{2016 \times 100}{112} \]
Calculating this gives:
\[ X = \frac{201600}{112} = 1800 \]
So, the marked price is Rs 1800.

### Step 4: Calculate the Tax Amount at 12%
Now, we find the amount of tax included in the price:
\[ \text{Tax} = 2016 - 1800 = 216 \]

### Step 5: Calculate the New Tax Amount at 7%
Next, we calculate the tax amount if the tax rate is reduced to 7%:
\[ \text{New Tax} = 7\% \text{ of } 1800 = \frac{7}{100} \times 1800 = 126 \]

### Step 6: Determine How Much Less the Customer Will Pay
Now, we find out how much less the customer will pay:
\[ \text{Difference} = \text{Old Tax} - \text{New Tax} = 216 - 126 = 90 \]

### Final Answer
The customer will pay Rs 90 less if the tax is reduced to 7%.

### Summary of Steps
1. Set up the equation for marked price.
2. Solve for marked price \( X \).
3. Calculate the tax amount at 12%.
4. Calculate the new tax amount at 7%.
5. Find the difference in the amount paid by the customer.