A dealer allows `36%` discount on the marked price of an article and still gains `28%` .If the cost price of the article is reduced by `10%` , how much discount percent should he allow now so as to get the same percentage of profit as before ?

Options

A. `45.8%`
B. `54.2%`
C. `57.2%`
D. `42.4%`

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step 1: Assume the Cost Price (CP)
Let the cost price (CP) of the article be \( CP = 100 \) (we can assume any value for simplicity).

### Step 2: Calculate the Selling Price (SP) with 28% Profit
Since the dealer gains 28%, the selling price (SP) can be calculated as:
\[ SP = CP + 28\% \text{ of } CP = 100 + 28 = 128 \]

### Step 3: Determine the Marked Price (MP)
The dealer allows a discount of 36% on the marked price (MP). Let the marked price be \( MP = X \).
The selling price after applying the discount can be expressed as:
\[ SP = MP - \text{Discount} = X - 0.36X = 0.64X \]
Setting this equal to the selling price we calculated:
\[ 0.64X = 128 \]

### Step 4: Solve for the Marked Price (MP)
To find \( X \):
\[ X = \frac{128}{0.64} = 200 \]
So, the marked price \( MP = 200 \).

### Step 5: Calculate the New Cost Price (CP)
If the cost price is reduced by 10%, the new cost price becomes:
\[ \text{New CP} = 100 - 10\% \text{ of } 100 = 100 - 10 = 90 \]

### Step 6: Calculate the Selling Price (SP) for the Same Profit Percentage
To maintain the same profit percentage of 28% on the new cost price:
\[ \text{Profit} = 28\% \text{ of New CP} = 0.28 \times 90 = 25.2 \]
Thus, the new selling price becomes:
\[ \text{New SP} = \text{New CP} + \text{Profit} = 90 + 25.2 = 115.2 \]

### Step 7: Calculate the Discount Required
Now, we need to find the discount percentage on the marked price to achieve this new selling price:
\[ \text{Discount} = MP - \text{New SP} = 200 - 115.2 = 84.8 \]

### Step 8: Calculate the Discount Percentage
The discount percentage can be calculated as:
\[ \text{Discount Percentage} = \left(\frac{\text{Discount}}{MP}\right) \times 100 = \left(\frac{84.8}{200}\right) \times 100 = 42.4\% \]

### Final Answer
The dealer should allow a discount of **42.4%** to achieve the same profit percentage as before.

---