If toffees are bought at the rate of 7 for Rs. 6, at what rate per hundred must they be sold to gain 33%?

Step 1: First, we need to find the cost price of 100 toffees. If 7 toffees cost Rs. 6, then 1 toffee costs Rs. 6/7. Therefore, 100 toffees would cost Rs. 6/7 * 100 = Rs. 85.71 (approximately).

Step 2: Next, we need to calculate the selling price for 100 toffees to gain a profit of 33%. The formula to calculate the selling price is: Selling Price = Cost Price + Profit.

Step 3: We know that Profit = (Profit Percentage/100) * Cost Price. Substituting the given profit percentage of 33% and the cost price of Rs. 85.71, we get Profit = (33/100) * 85.71 = Rs. 28.28 (approximately).

Step 4: Now, we can calculate the selling price. Selling Price = Cost Price + Profit = Rs. 85.71 + Rs. 28.28 = Rs. 113.99 (approximately).

So, to gain a profit of 33%, the toffees must be sold at the rate of approximately Rs. 114 per hundred.