A businessman allows a discount of 10% on the marked price. What percent above the cost price must he mark his goods to make a profit of 17 per cent ?

Options

A. 0.27
B. 0.18
C. 0.3
D. 0.2

Answer

To solve the problem step by step, let's break it down:

### Step 1: Define the Variables
Let the Cost Price (CP) be 100 (this is a convenient assumption to simplify calculations).

### Step 2: Calculate the Selling Price (SP)
The businessman wants to make a profit of 17%. Therefore, the Selling Price (SP) can be calculated as:
\[ SP = CP + \text{Profit} = 100 + 17\% \text{ of } 100 = 100 + 17 = 117 \]

### Step 3: Understand the Discount
The businessman allows a discount of 10% on the Marked Price (MP). This means:
\[ SP = MP - \text{Discount} \]
The discount can be expressed as:
\[ \text{Discount} = 10\% \text{ of } MP = 0.1 \times MP \]

### Step 4: Set Up the Equation
From the previous step, we can set up the equation:
\[ SP = MP - 0.1 \times MP \]
This simplifies to:
\[ SP = 0.9 \times MP \]

### Step 5: Substitute SP into the Equation
Now we substitute the value of SP we calculated earlier:
\[ 117 = 0.9 \times MP \]

### Step 6: Solve for MP
To find MP, divide both sides by 0.9:
\[ MP = \frac{117}{0.9} = 130 \]

### Step 7: Calculate the Percentage Above Cost Price
Now we need to find out how much the Marked Price (MP) is above the Cost Price (CP):
\[ \text{Difference} = MP - CP = 130 - 100 = 30 \]
To find the percentage above the Cost Price:
\[ \text{Percentage above CP} = \left(\frac{\text{Difference}}{CP}\right) \times 100 = \left(\frac{30}{100}\right) \times 100 = 30\% \]

### Final Answer
The businessman must mark his goods 30% above the cost price to make a profit of 17%.

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