A shopkeeper earns a profit of 25% when he sells an article by allowing 20% discount on its marked price. If the cost price of the article is decreased by 20%, how much discount percent should he allow now on the same marked price so as to earn the same percentage of profit as earlier ?
(a)`32%`
(b)`36%`
(c)`35%`
(d)`40%`

Options

A. `32%`
B. `36%`
C. `35%`
D. `40%`

Answer

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

### Step 1: Determine the Marked Price (MP) and Selling Price (SP)
Let's assume the marked price (MP) of the article is 100.

- Given that the shopkeeper allows a discount of 20% on the marked price:
\[ \text{Discount} = 20\% \text{ of } 100 = 20 \]
- Therefore, the selling price (SP) after the discount is:
\[ SP = MP - \text{Discount} = 100 - 20 = 80 \]

### Step 2: Calculate the Cost Price (CP)
The shopkeeper earns a profit of 25% on the cost price. We can express this relationship as:
\[ SP = CP + \text{Profit} \]
Where profit is 25% of CP. Thus:
\[ SP = CP + 0.25 \times CP = 1.25 \times CP \]
Substituting the SP we found:
\[ 80 = 1.25 \times CP \]
To find CP, we rearrange the equation:
\[ CP = \frac{80}{1.25} = 64 \]

### Step 3: Calculate the New Cost Price (CP) after a 20% Decrease
If the cost price is decreased by 20%, the new cost price (CP') will be:
\[ CP' = CP - 20\% \text{ of } CP = 64 - 0.20 \times 64 = 64 - 12.8 = 51.2 \]

### Step 4: Determine the Required Selling Price (SP') to Maintain the Same Profit Percentage
To maintain the same profit percentage of 25% on the new cost price:
\[ SP' = CP' + 25\% \text{ of } CP' = CP' + 0.25 \times CP' \]
This can be simplified to:
\[ SP' = 1.25 \times CP' = 1.25 \times 51.2 = 64 \]

### Step 5: Calculate the New Discount Percentage
Now, we need to find the discount percentage on the same marked price (MP = 100) to achieve the new selling price (SP' = 64):
- The discount amount is:
\[ \text{Discount} = MP - SP' = 100 - 64 = 36 \]
- The discount percentage is calculated as:
\[ \text{Discount Percentage} = \left(\frac{\text{Discount}}{MP}\right) \times 100 = \left(\frac{36}{100}\right) \times 100 = 36\% \]

### Final Answer
Thus, the discount percentage that should be allowed now on the same marked price to earn the same percentage of profit as earlier is:
\[ \boxed{36\%} \]