A shopkeeper allows 10% discount on goods when he sells without credit. Cost price of his goods is 80% of his selling price. If he sells his goods by cash, then his profit is

Options

A. `50%`
B. `70%`
C. `25%`
D. `40%`

Answer

To solve the problem step by step, we need to find the profit percentage when the shopkeeper sells his goods for cash after allowing a 10% discount.

### Step 1: Define the Selling Price (SP)
Let’s denote the Selling Price (SP) of the goods as \( SP \).

### Step 2: Calculate the Marked Price (MP)
Since the shopkeeper allows a 10% discount on the marked price, we can express the selling price in terms of the marked price (MP):
\[ SP = MP - (10\% \text{ of } MP) = MP - 0.1 \times MP = 0.9 \times MP \]
Thus, we can write:
\[ SP = 0.9 \times MP \]

### Step 3: Relate Cost Price (CP) to Selling Price (SP)
According to the problem, the cost price (CP) of the goods is 80% of the selling price:
\[ CP = 0.8 \times SP \]

### Step 4: Substitute SP in the CP equation
Now, substituting the expression for SP from Step 2 into the CP equation:
\[ CP = 0.8 \times (0.9 \times MP) = 0.72 \times MP \]

### Step 5: Calculate Profit
Profit can be calculated as:
\[ \text{Profit} = SP - CP \]
Substituting the values of SP and CP:
\[ \text{Profit} = SP - CP = SP - (0.72 \times MP) \]
Now substituting \( SP = 0.9 \times MP \):
\[ \text{Profit} = (0.9 \times MP) - (0.72 \times MP) = (0.9 - 0.72) \times MP = 0.18 \times MP \]

### Step 6: Calculate Profit Percentage
To find the profit percentage, we use the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{CP}\right) \times 100 \]
Substituting the values we have:
\[ \text{Profit Percentage} = \left(\frac{0.18 \times MP}{0.72 \times MP}\right) \times 100 \]
The \( MP \) cancels out:
\[ \text{Profit Percentage} = \left(\frac{0.18}{0.72}\right) \times 100 = 25\% \]

### Final Answer
Thus, the profit percentage when the shopkeeper sells his goods for cash is **25%**.

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