A vendor bought apples at 6 for ₹55 and oranges at 6 for ₹50. He bought four times as many apples as oranges. One-fortieth of the apples and seven-twentieths of the oranges got spoilt. He sold the rest of the apples at ₹12 per piece and the oranges at ₹10 per piece. The overall profit made by him is _____. % % % %

Sure, let's break this down step by step:

1. First, let's find out the cost price of each apple and orange. The vendor bought apples at 6 for ₹55, so the cost price of each apple is ₹55/6 = ₹9.17 (approximately). Similarly, he bought oranges at 6 for ₹50, so the cost price of each orange is ₹50/6 = ₹8.33 (approximately).

2. The vendor bought four times as many apples as oranges. Let's assume he bought 'x' oranges. Therefore, he bought '4x' apples.

3. One-fortieth of the apples and seven-twentieths of the oranges got spoilt. So, the number of apples that got spoilt is 4x/40 = x/10 and the number of oranges that got spoilt is 7x/20.

4. The vendor sold the rest of the apples at ₹12 per piece and the oranges at ₹10 per piece. So, the number of apples sold is 4x - x/10 = 3.9x and the number of oranges sold is x - 7x/20 = 0.65x.

5. The total cost price is (4x * cost price of each apple) + (x * cost price of each orange) = (4x * ₹9.17) + (x * ₹8.33).

6. The total selling price is (number of apples sold * selling price of each apple) + (number of oranges sold * selling price of each orange) = (3.9x * ₹12) + (0.65x * ₹10).

7. The profit is the total selling price - the total cost price.

8. The profit percentage is (profit / total cost price) * 100.

Without the actual number of oranges 'x', we can't calculate the exact profit. However, we can say that the profit percentage will be positive because the selling price of each apple and orange is higher than their cost price.