A shopkeeper allow 25% discount on mark price and earn 30% profit. If he gets 90 profit. Find the amount of the discount.

Options

A. a)Rs 130
B. b)Rs 125
C. c)Rs 190
D. d)Rs 140

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the given information
- The shopkeeper allows a 25% discount on the marked price (MP).
- He earns a 30% profit on the cost price (CP).
- The profit earned is ₹90.

### Step 2: Calculate the Cost Price (CP)
Since the profit is 30% of the CP and the profit earned is ₹90, we can set up the equation:
\[ \text{Profit} = \frac{30}{100} \times \text{CP} = 90 \]
To find the CP, we rearrange the equation:
\[ \text{CP} = \frac{90 \times 100}{30} = 300 \text{ rupees} \]

### Step 3: Calculate the Selling Price (SP)
The selling price (SP) can be calculated by adding the profit to the cost price:
\[ \text{SP} = \text{CP} + \text{Profit} = 300 + 90 = 390 \text{ rupees} \]

### Step 4: Relate SP to Marked Price (MP)
The selling price is also related to the marked price through the discount. Since the shopkeeper gives a 25% discount, the selling price is 75% of the marked price:
\[ \text{SP} = 75\% \text{ of MP} = \frac{75}{100} \times \text{MP} \]
We can set up the equation:
\[ 390 = \frac{75}{100} \times \text{MP} \]

### Step 5: Solve for Marked Price (MP)
To find the marked price, rearranging the equation gives:
\[ \text{MP} = \frac{390 \times 100}{75} = 520 \text{ rupees} \]

### Step 6: Calculate the Discount Amount
The discount amount is 25% of the marked price:
\[ \text{Discount} = \frac{25}{100} \times \text{MP} = \frac{25}{100} \times 520 = 130 \text{ rupees} \]

### Conclusion
The amount of the discount is ₹130.

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