By how much amount M.P. should exceed to C.P. in order to earn profit of 17% even after giving discount of 10% .

Answer

To solve the problem of how much the Mark Price (M.P.) should exceed the Cost Price (C.P.) in order to earn a profit of 17% after giving a discount of 10%, we can follow these steps:

### Step 1: Understand the relationship between M.P., C.P., profit, and discount.
We know that:
- Profit Percentage = (M.P. - C.P.) / C.P. * 100
- Discount Percentage = (M.P. - Selling Price) / M.P. * 100

### Step 2: Set up the equations based on the given percentages.
Let:
- C.P. = 100 (for simplicity)
- Profit = 17%, so M.P. needs to be calculated.
- Discount = 10%

### Step 3: Calculate the Selling Price (S.P.) after discount.
Since the discount is 10%, the Selling Price can be calculated as:
\[ S.P. = M.P. - (10\% \text{ of } M.P.) \]
\[ S.P. = M.P. \times (1 - 0.10) = M.P. \times 0.90 \]

### Step 4: Set up the profit equation.
We know that to earn a profit of 17%, the Selling Price must also be related to the Cost Price:
\[ S.P. = C.P. + (17\% \text{ of } C.P.) \]
\[ S.P. = 100 + (17\% \text{ of } 100) = 100 + 17 = 117 \]

### Step 5: Equate the two expressions for Selling Price.
From Step 3 and Step 4, we have:
\[ M.P. \times 0.90 = 117 \]

### Step 6: Solve for M.P.
To find M.P., we rearrange the equation:
\[ M.P. = \frac{117}{0.90} \]
\[ M.P. = 130 \]

### Step 7: Calculate how much M.P. exceeds C.P.
Now, we find how much M.P. exceeds C.P.:
\[ \text{Excess} = M.P. - C.P. = 130 - 100 = 30 \]

### Step 8: Calculate the percentage by which M.P. exceeds C.P.
To find the percentage by which M.P. exceeds C.P.:
\[ \text{Percentage} = \left(\frac{\text{Excess}}{C.P.}\right) \times 100 = \left(\frac{30}{100}\right) \times 100 = 30\% \]

### Final Answer:
M.P. should exceed C.P. by **30%**.

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