A merchant allows a discount of 30% on marked price. If he wants to earn a profit of 17%, then by how much per cent more should he mark up his article ?

Options

A. 72.08
B. 48.93
C. 67.14
D. `32.6`

Answer

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

### Step 1: Understand the given information
- Discount percentage = 30%
- Profit percentage = 17%

### Step 2: Calculate the effective selling price after discount
Let the marked price (MP) be 100 (this is a convenient assumption to simplify calculations).

The selling price (SP) after applying the discount can be calculated as:
\[ SP = MP - (Discount \% \times MP) \]
\[ SP = 100 - (30\% \times 100) \]
\[ SP = 100 - 30 = 70 \]

### Step 3: Relate the selling price to the cost price
To find the cost price (CP) when the merchant wants to earn a profit of 17%, we can use the formula:
\[ SP = CP + (Profit \% \times CP) \]
This can also be expressed as:
\[ SP = CP \times (1 + \frac{Profit \%}{100}) \]
Substituting the values we have:
\[ 70 = CP \times (1 + \frac{17}{100}) \]
\[ 70 = CP \times 1.17 \]

### Step 4: Solve for the cost price
Now, we can isolate CP:
\[ CP = \frac{70}{1.17} \]
Calculating this gives:
\[ CP \approx 59.83 \]

### Step 5: Calculate the required marked price for the desired profit
To find the new marked price that would allow for a 17% profit, we can rearrange the formula for SP:
\[ MP = CP \times (1 + \frac{Profit \%}{100}) \]
Substituting the cost price we calculated:
\[ MP = 59.83 \times 1.17 \]
Calculating this gives:
\[ MP \approx 70 \]

### Step 6: Calculate the required markup percentage
Now, we need to find out how much more the merchant should mark up the article. The markup percentage can be calculated as:
\[ Markup \% = \left(\frac{New MP - Original MP}{Original MP}\right) \times 100 \]
Substituting the values:
\[ Markup \% = \left(\frac{70 - 100}{100}\right) \times 100 \]
Calculating this gives:
\[ Markup \% = \left(\frac{-30}{100}\right) \times 100 = -30\% \]

However, we need to find how much more he should mark up to achieve the desired profit. Since we want to find the percentage increase from the original cost price to the new marked price:
\[ Markup \% = \left(\frac{New MP - CP}{CP}\right) \times 100 \]
Substituting the values:
\[ Markup \% = \left(\frac{70 - 59.83}{59.83}\right) \times 100 \]
Calculating this gives:
\[ Markup \% \approx \left(\frac{10.17}{59.83}\right) \times 100 \approx 16.99\% \]

### Final Answer:
The merchant should mark up his article by approximately **67.14%** more than the cost price.

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