A dealer sells an article by allowing a 15% discount on its marked price and gains 12% If the cost price of the article is increased by 10%.. how much discount percentage should be allow now on the same marked price so as to earn the same percentage of profit as before?

Options

A. A)`75%`
B. B)`6.5%`
C. C)`7.5%`
D. D)`6%`

Answer

To solve the problem step by step, we need to determine the new discount percentage that should be allowed on the same marked price in order to maintain the same profit percentage after the cost price has increased by 10%.

### Step 1: Understand the initial conditions
- The dealer sells an article with a **15% discount** on the marked price (MP).
- The dealer gains a **12% profit** on the cost price (CP).

### Step 2: Set up the initial formula
Using the formula:
\[ \frac{CP}{MP} = \frac{100 - \text{Discount Percentage}}{100 + \text{Profit Percentage}} \]
we can substitute the known values:
\[ \frac{CP}{MP} = \frac{100 - 15}{100 + 12} = \frac{85}{112} \]

### Step 3: Express CP in terms of MP
Let’s express CP in terms of MP:
\[ CP = \frac{85}{112} \times MP \]

### Step 4: Calculate the new cost price after a 10% increase
The new cost price (CP') after a 10% increase is:
\[ CP' = CP + 10\% \text{ of } CP = CP \times 1.10 = \left(\frac{85}{112} \times MP\right) \times 1.10 = \frac{85 \times 1.10}{112} \times MP = \frac{93.5}{112} \times MP \]

### Step 5: Set up the new discount formula
Now, we want to find the new discount percentage (D2) that allows the dealer to maintain the same profit percentage (12%). Using the same formula:
\[ \frac{CP'}{MP} = \frac{100 - D2}{100 + 12} \]
Substituting CP':
\[ \frac{\frac{93.5}{112} \times MP}{MP} = \frac{100 - D2}{112} \]
This simplifies to:
\[ \frac{93.5}{112} = \frac{100 - D2}{112} \]

### Step 6: Solve for D2
Since the denominators are the same, we can equate the numerators:
\[ 93.5 = 100 - D2 \]
Rearranging gives:
\[ D2 = 100 - 93.5 = 6.5 \]

### Conclusion
The new discount percentage that should be allowed on the same marked price to earn the same percentage of profit as before is **6.5%**.