A shopkeeper marks up price of an article by 60% above cost price and allow 25% discount on it. If shopkeeper marks up article by 75% above cost price and allow 20% discount on it, then find later profit is what percent more than earlier profit?

Options

A. `112.5%`
B. `125%`
C. `100%`
D. `75%`

Answer

To solve the problem step by step, we will calculate the cost price, marked price, selling price, and profit for both conditions described in the question.

### Step 1: Define the Cost Price
Let the cost price (CP) of the article be \(100\) (this is an arbitrary choice to simplify calculations).

### Step 2: Calculate the Marked Price for the First Condition
In the first condition, the shopkeeper marks up the price by \(60\%\) above the cost price.
- Marked Price (MP) = CP + \(60\%\) of CP
- MP = \(100 + 60\% \times 100 = 100 + 60 = 160\)

### Step 3: Calculate the Selling Price for the First Condition
The shopkeeper allows a \(25\%\) discount on the marked price.
- Selling Price (SP) = MP - \(25\%\) of MP
- SP = \(160 - 25\% \times 160 = 160 - 40 = 120\)

### Step 4: Calculate the Profit for the First Condition
Profit is calculated as:
- Profit = SP - CP
- Profit = \(120 - 100 = 20\)

### Step 5: Calculate the Profit Percentage for the First Condition
Profit Percentage = \(\frac{Profit}{CP} \times 100\)
- Profit Percentage = \(\frac{20}{100} \times 100 = 20\%\)

### Step 6: Calculate the Marked Price for the Second Condition
In the second condition, the shopkeeper marks up the price by \(75\%\) above the cost price.
- Marked Price (MP) = CP + \(75\%\) of CP
- MP = \(100 + 75\% \times 100 = 100 + 75 = 175\)

### Step 7: Calculate the Selling Price for the Second Condition
The shopkeeper allows a \(20\%\) discount on the marked price.
- Selling Price (SP) = MP - \(20\%\) of MP
- SP = \(175 - 20\% \times 175 = 175 - 35 = 140\)

### Step 8: Calculate the Profit for the Second Condition
Profit is calculated as:
- Profit = SP - CP
- Profit = \(140 - 100 = 40\)

### Step 9: Calculate the Profit Percentage for the Second Condition
Profit Percentage = \(\frac{Profit}{CP} \times 100\)
- Profit Percentage = \(\frac{40}{100} \times 100 = 40\%\)

### Step 10: Calculate the Increase in Profit
Now, we need to find out how much later profit is more than earlier profit.
- Increase in Profit = Later Profit - Earlier Profit
- Increase in Profit = \(40 - 20 = 20\)

### Step 11: Calculate the Percentage Increase in Profit
Percentage Increase = \(\frac{Increase in Profit}{Earlier Profit} \times 100\)
- Percentage Increase = \(\frac{20}{20} \times 100 = 100\%\)

### Final Answer
The later profit is \(100\%\) more than the earlier profit.

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