a trader bought 150eggs for 22.50 ; eggs were cracked . he sold the cracked eggs at 10 each and the rest at 17 each. what was his percentage gain ?.
150-30 = 120 good eggs.
Income = 120*0.17 + 30*0.1 =
Gain = Income-22.50 =
%Gain = (Gain/22.50)*100% =
22.50-120 ans 97.5
97.5
To find the trader's percentage gain, we need to calculate the difference between the selling price and the cost price (total amount spent on buying the eggs), and then calculate its percentage.
Let's break down the problem step by step:
1. Calculate the cost price of all the eggs:
The trader bought 150 eggs for $22.50. So, the cost price per egg can be found by dividing the total cost by the number of eggs:
Cost price per egg = Total cost / Number of eggs
= $22.50 / 150
= $0.15 (rounded to 2 decimal places)
2. Calculate the cost price of the cracked eggs:
The problem doesn't specify the number of cracked eggs, so let's assume 'x' represents the number of cracked eggs. Since the trader bought 150 eggs in total, the remaining non-cracked eggs would be 150 - x.
The cost of cracked eggs can be calculated by multiplying the number of cracked eggs by the cost price per egg:
Cost of cracked eggs = Number of cracked eggs * Cost price per egg
= x * $0.15
= $0.15x
3. Calculate the selling price of the cracked eggs:
The trader sold the cracked eggs at $10 each. So, the total selling price of the cracked eggs can be found by multiplying the selling price per egg by the number of cracked eggs:
Selling price of cracked eggs = Number of cracked eggs * Selling price per egg
= x * $10
= $10x
4. Calculate the cost price of the remaining eggs:
As mentioned earlier, the remaining non-cracked eggs would be 150 - x.
The cost of the remaining eggs can be calculated by multiplying the number of remaining eggs by the cost price per egg:
Cost of remaining eggs = Number of remaining eggs * Cost price per egg
= (150 - x) * $0.15
= $0.15(150 - x)
= $22.50 - $0.15x
5. Calculate the selling price of the remaining eggs:
The trader sold the remaining eggs at $17 each. So, the total selling price of the remaining eggs can be found by multiplying the selling price per egg by the number of remaining eggs:
Selling price of remaining eggs = Number of remaining eggs * Selling price per egg
= (150 - x) * $17
= $17(150 - x)
= $2550 - $17x
6. Calculate the total selling price:
The total selling price is the sum of the selling price of the cracked eggs and the selling price of the remaining eggs:
Total selling price = Selling price of cracked eggs + Selling price of remaining eggs
= $10x + ($2550 - $17x)
= $2550 - $7x
7. Calculate the gain (profit):
The gain is calculated by subtracting the cost price from the total selling price:
Gain = Total selling price - Cost price
= ($2550 - $7x) - ($22.50 - $0.15x)
= $2550 - $7x - $22.50 + $0.15x
= $2527.50 - $6.85x
8. Calculate the percentage gain:
Percentage gain is calculated by dividing the gain by the cost price and then multiplying by 100:
Percentage gain = (Gain / Cost price) * 100
= (($2527.50 - $6.85x) / $22.50) * 100
To get the specific percentage gain, we need to know the value of 'x', the number of cracked eggs.