A shopkeeper marks his article `50%` above the cost price and gives a discount of `20%` on it. If he had marked his article `75%` above the cost price and had given a discount of `20%` on it, then find the earlier profit is what per cent of the profit earned latter?

Options

A. `50%`
B. `60%`
C. `33 1/3%`
D. `40%`

Answer

To solve the problem step by step, we will break it down into two cases based on the given conditions.

### Step 1: Define the Cost Price (CP)
Let's assume the Cost Price (CP) of the article is ₹100.

### Step 2: Calculate the Marked Price (MP) for the First Case
In the first case, the shopkeeper marks his article 50% above the cost price.
- Marked Price (MP) = CP + 50% of CP
- MP = 100 + (50/100) * 100 = 100 + 50 = ₹150

### Step 3: Calculate the Selling Price (SP) for the First Case
The shopkeeper gives a discount of 20% on the marked price.
- Discount = 20% of MP = (20/100) * 150 = ₹30
- Selling Price (SP) = MP - Discount = 150 - 30 = ₹120

### Step 4: Calculate the Profit for the First Case
Profit = Selling Price - Cost Price
- Profit = 120 - 100 = ₹20

### Step 5: Calculate the Marked Price (MP) for the Second Case
In the second case, the shopkeeper marks his article 75% above the cost price.
- Marked Price (MP) = CP + 75% of CP
- MP = 100 + (75/100) * 100 = 100 + 75 = ₹175

### Step 6: Calculate the Selling Price (SP) for the Second Case
The shopkeeper again gives a discount of 20% on the marked price.
- Discount = 20% of MP = (20/100) * 175 = ₹35
- Selling Price (SP) = MP - Discount = 175 - 35 = ₹140

### Step 7: Calculate the Profit for the Second Case
Profit = Selling Price - Cost Price
- Profit = 140 - 100 = ₹40

### Step 8: Calculate the Required Percentage
We need to find out what percentage the earlier profit (from the first case) is of the profit earned later (from the second case).
- Required Percentage = (Earlier Profit / Later Profit) * 100
- Required Percentage = (20 / 40) * 100 = 50%

### Conclusion
The earlier profit is 50% of the profit earned later.