a vendor sold 100 fresh chicken eggs. eight of them were sold at a profit of 30% while the rest were sold at a loss of 40%. what is the percentage gain or loss on the whole stock?
unit cost price .... x
return = 1.3(8) + .6(92)
= 65.6
percentage = 65.6/100 = 65.6%
So there is a loss of 34.4%
test:
suppose he bought them at $1 per egg
cost price = $100
return = 8(1.30) + 92(.60) = 10.40 + 55.20
= $65.60
He lost $34.40 out of the $100 he spent.
So loss is 34.4%
To calculate the percentage gain or loss on the whole stock, we need to find the total cost price (CP) and the total selling price (SP).
Let's calculate the profit made on the eggs sold at a 30% profit first.
Number of eggs sold at 30% profit = 8
Profit percentage = 30% = 0.30
Profit made on each egg = CP x Profit percentage
Since the profit is 30%, the selling price is 100% + 30% = 130% of the cost price. So, the profit made is 30% of the cost price.
Let's assume the cost price of each egg to be C.
Profit made on each egg = C x 0.30
Total profit made on eggs sold at 30% profit = Profit made on each egg x Number of eggs sold at 30% profit
= (C x 0.30) x 8
Next, let's calculate the loss made on the eggs sold at a loss of 40%.
Number of eggs sold at 40% lost = Total eggs sold - Eggs sold at 30% profit
= 100 - 8 = 92
Loss percentage = 40% = 0.40
Loss made on each egg = CP x Loss percentage
Since the selling price is 100% - 40% = 60% of the cost price, the loss made is 40% of the cost price.
Let's assume the cost price of each egg to be C.
Loss made on each egg = C x 0.40
Total loss made on eggs sold at 40% loss = Loss made on each egg x Number of eggs sold at 40% loss
= (C x 0.40) x 92
The total selling price (SP) is:
SP = Selling price of eggs sold at profit + Selling price of eggs sold at loss
= (CP + Profit made on each egg x Number of eggs sold at 30% profit) + (CP - Loss made on each egg x Number of eggs sold at 40% loss)
= (CP + (C x 0.30) x 8) + (CP - (C x 0.40) x 92)
= CP + 8C x 0.30 + CP - 92C x 0.40
= 2CP - 36.8C
We know that SP = CP - Loss.
CP - Loss = 2CP - 36.8C
Rearranging the equation, we have:
36.8C - CP = Loss
Percentage loss = (Loss / CP) x 100
Percentage loss = ((36.8C - CP) / CP) x 100
Percentage gain or loss on the whole stock = Percentage loss
= ((36.8C - CP) / CP) x 100
However, we don't have a specific value for the cost price (C) of each egg. Therefore, we cannot determine the exact percentage gain or loss on the whole stock without this information.
To calculate the percentage gain or loss on the whole stock, we need to determine the total cost and the total revenue for the eggs sold.
Let's break down the information given:
1. Profit of 30% on 8 chicken eggs:
To calculate the selling price of these eggs, we need to add 30% of the cost to the original cost. Since the profit is 30%, the selling price will be 100% + 30% = 130% of the original cost.
2. Loss of 40% on the remaining eggs (92 eggs):
To calculate the selling price of these eggs, we deduct 40% of the cost from the original cost. Since the loss is 40%, the selling price will be 100% - 40% = 60% of the original cost.
Now, let's calculate the revenue:
For the 8 eggs sold at a profit:
Revenue from these 8 eggs = 8 eggs * 130% of the original cost
For the remaining 92 eggs sold at a loss:
Revenue from these 92 eggs = 92 eggs * 60% of the original cost
Next, we need to calculate the original cost:
Original cost for the 100 eggs = Cost per egg * Number of eggs sold
Finally, let's calculate the percentage gain or loss on the whole stock:
Percentage gain or loss = [(Total revenue - Total cost) / Total cost] * 100
Now that we have the steps, we can use the given information to calculate the percentage gain or loss on the whole stock.