A shopkeeper sets MRP of a product such that after giving 10% discount, he earns 12.5% profit. What will be his profit/loss percent if he allows a discount of 25%?

Options

A. A)`5%`
B. B)`10.45%`
C. C)`8.33%`
D. D)`6.25%`

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the relationship between Cost Price (CP), Marked Price (MP), Discount, and Selling Price (SP).
The relationship can be expressed using the formula:
\[ \frac{CP}{MP} = \frac{100 - \text{Discount \%}}{100 + \text{Profit \%}} \]

### Step 2: Substitute the known values for the first scenario.
Given:
- Discount = 10%
- Profit = 12.5%

Substituting these values into the formula:
\[ \frac{CP}{MP} = \frac{100 - 10}{100 + 12.5} = \frac{90}{112.5} \]

### Step 3: Simplify the ratio.
To simplify \(\frac{90}{112.5}\), we can multiply both the numerator and denominator by 10 to eliminate the decimal:
\[ \frac{90 \times 10}{112.5 \times 10} = \frac{900}{1125} \]
Now, simplifying this fraction gives:
\[ \frac{900 \div 225}{1125 \div 225} = \frac{4}{5} \]
This means the ratio of CP to MP is 4:5.

### Step 4: Assign a value to the Cost Price.
Let’s assume the Cost Price (CP) is 100. Then, using the ratio:
\[ MP = \frac{5}{4} \times CP = \frac{5}{4} \times 100 = 125 \]

### Step 5: Calculate the Selling Price (SP) for the second scenario with a 25% discount.
Now, we need to calculate the Selling Price when a 25% discount is applied to the Marked Price (MP):
\[ SP = MP \times (1 - \text{Discount \%}) = 125 \times (1 - 0.25) = 125 \times 0.75 = 93.75 \]

### Step 6: Calculate the Loss.
Now, we find the loss incurred:
\[ \text{Loss} = CP - SP = 100 - 93.75 = 6.25 \]

### Step 7: Calculate the Loss Percentage.
To find the loss percentage, we use the formula:
\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{CP}\right) \times 100 = \left(\frac{6.25}{100}\right) \times 100 = 6.25\% \]

### Conclusion:
The shopkeeper will incur a loss of **6.25%** if he allows a discount of 25%.

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