How much percent above the cost price should a shopkeeper mark his goods so that after allowing a discount of 25% on the marked price, he gains 20%?

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the Variables
Let the cost price (CP) of the goods be Rs. 100. We will denote the marked price (MP) as Rs. x.

### Step 2: Calculate Selling Price (SP) after Discount
The shopkeeper allows a discount of 25% on the marked price. Therefore, the selling price (SP) after the discount can be calculated as:
\[ SP = MP - (25\% \text{ of } MP) = x - 0.25x = 0.75x \]

### Step 3: Calculate the Desired Selling Price for a Profit
The shopkeeper wants to gain 20% on the cost price. Thus, the desired selling price (SP) can be calculated as:
\[ SP = CP + (20\% \text{ of } CP) = 100 + 0.20 \times 100 = 100 + 20 = Rs. 120 \]

### Step 4: Set Up the Equation
Now we can set the selling price from step 2 equal to the desired selling price from step 3:
\[ 0.75x = 120 \]

### Step 5: Solve for Marked Price (MP)
To find x, we will solve the equation:
\[ x = \frac{120}{0.75} = 160 \]

### Step 6: Calculate the Percentage Above Cost Price
Now we need to find out how much percent above the cost price the marked price is. The cost price is Rs. 100, and the marked price is Rs. 160. The percentage above the cost price can be calculated as:
\[ \text{Percentage} = \left(\frac{MP - CP}{CP}\right) \times 100 = \left(\frac{160 - 100}{100}\right) \times 100 = \left(\frac{60}{100}\right) \times 100 = 60\% \]

### Final Answer
The shopkeeper should mark his goods **60% above the cost price**.

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