A woman bought 130 kg of tomatoes for 4452,000.00. She sold half of the tomatoes at a profit of 30%. The rest of the tomatoes began to go bad, she then redu...

 A woman bought 130 kg of tomatoes for 4452,000.00. She sold half of the tomatoes at a profit of 30%. The rest of the tomatoes began to go bad, she then reduced the selling price per kg by 12%. Calculate:

(a) the new selling price per kg;

(ii) the percentage profit on the entire sales if she threw away 5 kg of bad tomatoes.

Answer Details

(a) Let's first find the cost per kilogram of the tomatoes:

Cost per kilogram = Total cost / Total weight
Cost per kilogram = 4452,000.00 / 130 kg
Cost per kilogram = 34,246.15

Now let's find the selling price per kilogram for the first half of the tomatoes, which were sold at a 30% profit:

Profit = Selling price - Cost price
30% of Cost price = 0.3 * 34,246.15 = 10,273.85
Selling price = Cost price + Profit
Selling price = 34,246.15 + 10,273.85 = 44,520.00
Selling price per kilogram = Selling price / (130 kg / 2)
Selling price per kilogram = 44,520.00 / 65 kg
Selling price per kilogram = 684.92

Now let's find the new selling price per kilogram for the remaining tomatoes, which were sold at a 12% discount:

Discount = Selling price before discount - Selling price after discount
12% of Selling price before discount = 0.12 * Selling price before discount
Selling price after discount = Selling price before discount - 0.12 * Selling price before discount
Selling price after discount = 0.88 * Selling price before discount
Selling price per kilogram = Selling price after discount / (130 kg / 2)
Selling price per kilogram = 0.88 * Selling price before discount / (130 kg / 2)
Selling price per kilogram = 0.44 * Selling price before discount / 65
Selling price per kilogram = 0.44 * 684.92 / 65
Selling price per kilogram = 4.63

(ii) If 5 kg of tomatoes were thrown away, then the total weight sold would be 125 kg. Let's calculate the total revenue:

Revenue = Selling price per kilogram * Total weight sold
Revenue = (684.92 * 65 / 2) + (4.63 * 60)
Revenue = 22,303.80

The cost of the tomatoes was 4452,000.00, and since the revenue was less than that, there was a loss. Let's calculate the percentage loss:

Loss = Cost - Revenue
Loss = 4452,000.00 - 22,303.80
Loss = 4429,696.20
Percentage loss = (Loss / Cost) * 100
Percentage loss = (4429,696.20 / 4452,000.00) * 100
Percentage loss = 99.5%

So the percentage profit on the entire sales was -99.5%, which means there was a loss of 99.5%.