Smith buys an article marked at Rs 2,200. The rate of tax is 12%. He asks the shopkeeper to reduce the price of the article to such an extent that he does not have to pay anything more than Rs 2.240 including tax. Calculate the reduction, as percent, needed in the marked price of the article.

Answer

To solve the problem step by step, we need to calculate the reduction in the marked price of the article that Smith wants to buy, so that he does not pay more than Rs 2,240 including tax.

### Step 1: Understand the problem
Smith wants to buy an article marked at Rs 2,200. The tax rate is 12%, and he wants the total price (including tax) to be Rs 2,240.

### Step 2: Set up the equation
Let the reduced price of the article be \( x \). The total cost including tax can be expressed as:
\[ \text{Total Cost} = x + \left(\frac{12}{100} \times x\right) = 2240 \]
This simplifies to:
\[ x + 0.12x = 2240 \]
\[ 1.12x = 2240 \]

### Step 3: Solve for \( x \)
To find \( x \), we can rearrange the equation:
\[ x = \frac{2240}{1.12} \]
Calculating this gives:
\[ x = 2000 \]

### Step 4: Calculate the reduction
The marked price of the article is Rs 2,200, and the reduced price is Rs 2,000. Therefore, the reduction in price is:
\[ \text{Reduction} = \text{Marked Price} - \text{Reduced Price} = 2200 - 2000 = 200 \]

### Step 5: Calculate the reduction percentage
To find the reduction percentage based on the marked price, we use the formula:
\[ \text{Reduction Percentage} = \left(\frac{\text{Reduction}}{\text{Marked Price}}\right) \times 100 \]
Substituting the values we have:
\[ \text{Reduction Percentage} = \left(\frac{200}{2200}\right) \times 100 \]
Calculating this gives:
\[ \text{Reduction Percentage} = \frac{200 \times 100}{2200} = \frac{20000}{2200} \approx 9.09\% \]

### Final Answer
The reduction needed in the marked price of the article is approximately \( 9.09\% \).

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