Giri sold a machine forRs46,000 with a discount of 16% on the labelled price and made a profit of 19.7%. What would have been the profit%, if the machine was sold at 28% discount on the labelled price?

Options

A. `2.6%`
B. `2.8%`
C. `2.5%`
D. `3.4%`

Answer

To solve the problem step by step, we need to determine the profit percentage if Giri sold the machine at a 28% discount on the labeled price. Here’s how we can do it:

### Step 1: Calculate the labeled price (LP)
Given that Giri sold the machine for Rs 46,000 with a discount of 16%, we can find the labeled price using the formula:

\[ \text{Selling Price} = \text{Labeled Price} \times \left(1 - \frac{\text{Discount}}{100}\right) \]

Substituting the values:

\[ 46000 = LP \times \left(1 - 0.16\right) \]
\[ 46000 = LP \times 0.84 \]
\[ LP = \frac{46000}{0.84} = 54761.90 \text{ (approximately)} \]

### Step 2: Calculate the cost price (CP)
Giri made a profit of 19.7% on the cost price. We can express this as:

\[ \text{Selling Price} = \text{Cost Price} \times \left(1 + \frac{\text{Profit}}{100}\right) \]

Substituting the values:

\[ 46000 = CP \times \left(1 + 0.197\right) \]
\[ 46000 = CP \times 1.197 \]
\[ CP = \frac{46000}{1.197} = 38407.18 \text{ (approximately)} \]

### Step 3: Calculate the new selling price (NSP) at 28% discount
Now, we need to find the new selling price if the discount is 28%. The new selling price can be calculated as follows:

\[ \text{New Selling Price} = LP \times \left(1 - \frac{28}{100}\right) \]
\[ \text{New Selling Price} = 54761.90 \times 0.72 \]
\[ \text{New Selling Price} = 39418.97 \text{ (approximately)} \]

### Step 4: Calculate the profit with the new selling price
Profit can be calculated as:

\[ \text{Profit} = \text{New Selling Price} - \text{Cost Price} \]
\[ \text{Profit} = 39418.97 - 38407.18 = 1011.79 \text{ (approximately)} \]

### Step 5: Calculate the profit percentage
Finally, we can find the profit percentage using the formula:

\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100 \]
\[ \text{Profit Percentage} = \left(\frac{1011.79}{38407.18}\right) \times 100 \approx 2.63\% \]

### Conclusion
If Giri sold the machine at a 28% discount on the labeled price, the profit percentage would be approximately **2.63%**.

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