An industrial fertilizer costing $370 per tonne to produce is sold retail 61 cents per kilogram.If there is a wastage of 2.5%,find the profit as a percentage of the cost?
First, you look at the cost for the production of the fertiliser, which is $370.
Then, you need to find the profit. To do this, you have to consider the 2.5% loss due to wastage. 100%- 2.5%= 97.5%.
Convert this into a fraction- 0.975, and make the units to the same: into tonnes. This is done by multiplying the 61 cents ($0.61) by 1000 (as 1000kg makes a tonne.
The equation: 0.975 * 1000 * 0.61. This equals to $594.75.
The profit is the amount gained. To find this, you subtract the production cost from the retail price. Therefore, 594.75- 370 = $224.75.
Lastly, to find the profit as a percentage of the cost, you put the profit over the cost as a fraction (224.75/370). 224.75 / 370= 0.6074324324.
Furthermore, convert the fraction to a percentage to a standard 2 decimal places. This equates to 60.74%.
Therefore, the profit as a percentage of the cost is 60.74%.
cost = 370
because of the 2.5% loss due to wastage, they only sold 97.5% of the fertilizer
return = .975(1000)(.61) = 584.75
profit = 224.75
Percentage profit = 224.75/370 = appr 60.7 %
To find the profit as a percentage of the cost, we need to calculate the profit first. Here's how you can do it:
Step 1: Convert the price per kilogram to the price per tonne.
Since there are 1000 kilograms in a tonne, we multiply the retail price of 61 cents per kilogram by 1000 to get the retail price per tonne.
Retail price per tonne = 61 cents per kilogram * 1000 kilograms per tonne = $610 per tonne.
Step 2: Calculate the cost per kilogram after considering the wastage.
Since there is a wastage of 2.5%, we need to calculate the effective cost per kilogram.
Effective cost per kilogram = (Cost per tonne / 100) * (100 - Wastage percentage)
Effective cost per kilogram = ($370 per tonne / 100) * (100 - 2.5%) = $361.75 per tonne / 1000 kilograms = $0.36175 per kilogram.
Step 3: Calculate the profit per kilogram.
Profit per kilogram = Retail price per kilogram - Effective cost per kilogram
Profit per kilogram = $0.61 per kilogram - $0.36175 per kilogram = $0.24825 per kilogram.
Step 4: Calculate the profit percentage of the cost.
Profit percentage of the cost = (Profit per kilogram / Effective cost per kilogram) * 100%
Profit percentage of the cost = ($0.24825 per kilogram / $0.36175 per kilogram) * 100% = 68.6%
Therefore, the profit as a percentage of the cost is approximately 68.6%.