A trader mixes Coffee A which costs $9 per kg with Coffee B which costs $13 per kg and Coffee C which costs $15 per kg, in the ratio 4:3:1. The mixture is then sold at $1.80 per 100 g. Express his profit or loss as a percentage of his cost price.
To find the cost price, we need to determine the amount of each coffee used in the mixture.
Let's assume the trader mixes 4x kg of Coffee A, 3x kg of Coffee B, and x kg of Coffee C, where x is a common multiple for simplicity.
The cost of 1 kg of Coffee A is $9, so the cost of 4x kg of Coffee A is 4x * $9 = $36x.
Similarly, the cost of 3x kg of Coffee B is 3x * $13 = $39x.
And the cost of x kg of Coffee C is x * $15 = $15x.
The total cost price is the sum of the individual costs: $36x + $39x + $15x = $90x.
The mixture is sold at $1.80 per 100 g, which is equivalent to $18 per kg.
The ratio of Coffee A: Coffee B: Coffee C is 4:3:1, so the total amount of coffee in the mixture is 4x + 3x + x = 8x kg.
Therefore, the selling price of the mixture is $18 * 8x = $144x.
Profit or loss is calculated by subtracting the cost price from the selling price: Profit/Loss = $144x - $90x = $54x.
To express the profit/loss as a percentage of the cost price, we divide the profit/loss by the cost price and multiply by 100:
Profit/Loss % = (Profit/Loss / Cost Price) * 100
= ($54x / $90x) * 100
= 60%
Therefore, the profit or loss, expressed as a percentage of the cost price, is 60%.
Coffee A : B : C = 4:3:1
= 4x : 3x : x , where these parts are expressed in kg
so he bought 8x kg of coffee
Cost of mixture = 9(4x) + 13(3x) + 15x = $90x
selling price = $1.80/100 g = $18 / kg
and he has 8x kg to sell
so return from sale = $18(8x)
profit = $(18(8x) - 90x) = $54x
percentage of profit = 54x / 90x = .6 = 60%
check:
suppose he bought 4kg, 3kg, and 1kg of the corresponding mixture
he bought this for 9(4) + 13(3) + 15 or a total of $90
so he has 8 kg so sell at 1.80/100 g or at $18/kg
return after sale = 18(8) = $144
profit = 144-90 = $54
percentage profit = 54/90 = .6 or 60%
Well, let me do some quick calculations to help you out with that.
First, let's figure out the cost price of the mixture per kilogram.
For every 4 kg of Coffee A, the cost is $9 x 4 = $36.
For every 3 kg of Coffee B, the cost is $13 x 3 = $39.
For every 1 kg of Coffee C, the cost is $15 x 1 = $15.
So the total cost price per kg is $36 + $39 + $15 = $90.
Next, let's convert the selling price of the mixture into dollars per kilogram.
$1.80 per 100 g is equivalent to $1.80 x 10 = $18 per kg.
Now, let's calculate the profit or loss as a percentage of the cost price.
Profit or loss % = (Selling Price - Cost Price)/Cost Price x 100
= ($18 - $90)/$90 x 100
= -$72/$90 x 100
= -80%
Oh dear, it seems our trader has made a loss of 80% of his cost price. I guess mixing coffee just isn't his cup of tea!
To answer this question, we need to calculate the cost price and selling price of the mixture first.
Suppose the trader mixes 4 kg of Coffee A, 3 kg of Coffee B, and 1 kg of Coffee C.
Cost price of Coffee A = $9 per kg
Cost price of Coffee B = $13 per kg
Cost price of Coffee C = $15 per kg
Total cost price of Coffee A = 4 kg * $9/kg = $36
Total cost price of Coffee B = 3 kg * $13/kg = $39
Total cost price of Coffee C = 1 kg * $15/kg = $15
Total cost price of the mixture = $36 + $39 + $15 = $90
The mixture is sold at $1.80 per 100 g. Since there are 1000 g in 1 kg, the selling price per kg is $1.80 * 10 = $18.
Profit or Loss = Selling Price - Cost Price
Profit or Loss = $18 - $90 = -$72
Since the profit is negative, it means there is a loss of $72.
Now, to express the loss as a percentage of the cost price, we can use the formula:
Percentage Loss = (Loss / Cost Price) * 100
Percentage Loss = (-$72 / $90) * 100
Percentage Loss ≈ -80%
Therefore, the trader's loss is approximately 80% of his cost price.