A man bought two types of apples, one at ₹2 for 3 apples and the other at ₹6 per apple. He purchased an equal number of each type and sold all the apples at ₹6 per apple. Find his percentage profit.

The correct option is 80%.

To find the percentage profit, let us break down the problem into simple steps by assuming a convenient number of apples purchased. Since the first type of apple is priced at ₹2 for 3 apples, choosing a multiple of 3 will make our calculations straightforward and free of fractions.

Let us assume the man purchased 3 apples of each type. Therefore, the total number of apples purchased is:
$$3+3=6\text{apples}$$

Step 1: Calculate the Total Cost Price (CP)
- Cost of 3 apples of the first type = ₹2
- Cost of the second type of apple is ₹6 per apple. Since he bought 3 apples of this type, their cost is:
$$3\times 6=₹18$$
- Total Cost Price (CP) for all 6 apples is:
$$\text{CP}=2+18=₹20$$

Step 2: Calculate the Total Selling Price (SP)
The man sells all 6 apples at the rate of ₹6 per apple. Therefore, the total Selling Price (SP) is:
$$\text{SP}=6\times 6=₹36$$

Step 3: Calculate the Profit
Profit is the difference between the Selling Price and the Cost Price:
$$\text{Profit}=\text{SP}-\text{CP}$$
$$\text{Profit}=36-20=₹16$$

Step 4: Calculate the Profit Percentage
The formula for profit percentage is:
$$\text{Profit Percentage}=\left(\frac{\text{Profit}}{\text{CP}}\right)\times 100$$
Substituting the values we calculated:
$$\text{Profit Percentage}=\left(\frac{16}{20}\right)\times 100$$
Simplifying the expression:
$$\text{Profit Percentage}=0.8\times 100=80\%$$