A shopkeeper gains 20% while buying the goods and 30% while selling them. Find his total gain per cent.

Options

A. 0.5
B. 0.36
C. 0.56
D. 0.4

Answer

To find the total gain percentage when a shopkeeper gains 20% while buying goods and 30% while selling them, we can follow these steps:

### Step 1: Understand the Gains
The shopkeeper gains:
- 20% on the cost price (CP) when buying goods.
- 30% on the selling price (SP) when selling goods.

### Step 2: Convert Percentages to Fractions
Convert the percentages into fractions:
- 20% = 20/100 = 1/5
- 30% = 30/100 = 3/10

### Step 3: Calculate Effective Gain
To find the total gain percentage, we can use the formula for successive percentage gains:
\[ \text{Total Gain} = \text{Gain}_1 + \text{Gain}_2 + \left(\frac{\text{Gain}_1 \times \text{Gain}_2}{100}\right) \]

Where:
- Gain_1 = 20%
- Gain_2 = 30%

### Step 4: Substitute the Values
Substituting the values into the formula:
\[ \text{Total Gain} = 20 + 30 + \left(\frac{20 \times 30}{100}\right) \]

### Step 5: Calculate the Product
Calculate the product:
\[ \frac{20 \times 30}{100} = \frac{600}{100} = 6 \]

### Step 6: Add the Gains
Now, add the gains together:
\[ \text{Total Gain} = 20 + 30 + 6 = 56\% \]

### Step 7: Conclusion
Thus, the total gain percentage for the shopkeeper is **56%**.

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