A man purchased two varieties of apples at the rate of ₹2 for 3 apples and ₹1 per apple, respectively. If he purchased an equal number of apples of each variety and then sold all his apples at ₹1 per apple, what was his profit percentage?

Correct option is B

Given:

Variety 1: 2 Rs for 3 apples. CP per apple = $$\frac{2}{3}$$​​

Variety 2: 1 Rs per apple.

Equal number of apples for both varieties.

Selling Price (SP): All apples sold at 1 Rs per apple.

Total Selling Price (SP):

$$\text{Total SP} = (\text{SP per apple}) \times (\text{Total number of apples})$$ 

Profit Percentage:

$$\text{Profit \%} = \left(\frac{\text{Total SP} - \text{Total CP}}{\text{Total CP}} \right) \times 100$$​​

Solution:  

Let the number of apples of each variety purchased =  n

Total CP:

​$$\text{Total CP} = \left(\frac{2}{3} \times n \right) + (1 \times n) = \frac{2n}{3} + n = \frac{5n}{3}$$

Total SP:

Total apples = 2n (since n apples from each variety).

​$$\text{Total SP} = 1 \times 2n = 2n$$​​

​$$\text{Profit} = \text{Total SP} - \text{Total CP} = 2n - \frac{5n}{3} = \frac{6n}{3} - \frac{5n}{3} = \frac{n}{3}​$$ 

Profit Percentage:

​$$\text{Profit \%} = \left(\frac{\frac{n}{3}}{\frac{5n}{3}}\right) \times 100 = \left(\frac{1}{5}\right) \times 100 = 20\%$$ 

The correct answer is option (b) 20 %