A shopkeeper purchases 50 dozen eggs at Rs. 16 per dozen. Of these 40 eggs were found to be broken. At what price should he sell the remaining eggs in order to make a profit of 5%?
To find the selling price of the remaining eggs, we need to calculate the cost price and then add the desired profit.
1. Calculate the cost price of the eggs:
The shopkeeper purchased 50 dozen eggs at Rs. 16 per dozen, so the total cost of purchasing all the eggs is:
50 dozen * Rs. 16 per dozen = Rs. 800
2. Calculate the number of remaining unbroken eggs:
Since there were 40 broken eggs, the total number of remaining unbroken eggs is:
50 dozen * 12 eggs per dozen - 40 broken eggs = 600 eggs - 40 broken eggs = 560 eggs
3. Calculate the cost price per egg for the remaining eggs:
Cost price per egg = total cost / total number of eggs
Cost price per egg = Rs. 800 / 560 eggs = Rs. 1.43 per egg (rounded to two decimal places)
4. Calculate the desired profit:
Profit = 5% of the cost price
Profit = 5/100 * Rs. 800 = Rs. 40
5. Calculate the selling price per egg:
Selling price per egg = cost price per egg + profit
Selling price per egg = Rs. 1.43 per egg + Rs. 40 / 560 eggs
Selling price per egg = Rs. 1.43 + Rs. 0.07 = Rs. 1.50 per egg
Therefore, the shopkeeper should sell the remaining eggs at Rs. 1.50 per egg to make a profit of 5%.
To find the price at which the shopkeeper should sell the remaining eggs, we need to follow a step-by-step approach:
1. Calculate the total cost of 50 dozen eggs:
The shopkeeper purchased 50 dozen eggs at Rs. 16 per dozen.
So, the total cost = 50 dozen * Rs. 16/dozen = Rs. 800
2. Calculate the cost of broken eggs:
Out of the 50 dozen eggs, 40 eggs were found to be broken.
As there are 12 eggs in each dozen, the total number of broken eggs = 40 eggs.
Therefore, the cost of broken eggs = 40 eggs * Rs. 16/dozen = Rs. 80
3. Calculate the cost of remaining eggs:
As there are 12 eggs in each dozen, the total number of remaining eggs = (50 dozen * 12) - 40 eggs = 600 eggs.
The remaining eggs' cost can be calculated as the total cost minus the cost of broken eggs:
Cost of remaining eggs = Total cost - Cost of broken eggs = Rs. 800 - Rs. 80 = Rs. 720
4. Calculate the desired profit:
The shopkeeper wants to make a profit of 5%.
So, the desired profit = 5% of the cost of remaining eggs = (5/100) * Rs. 720 = Rs. 36
5. Calculate the selling price of the remaining eggs:
The selling price of the remaining eggs will be the cost of remaining eggs plus the desired profit:
Selling price = Cost of remaining eggs + Desired profit = Rs. 720 + Rs. 36 = Rs. 756
Therefore, the shopkeeper should sell the remaining eggs at a price of Rs. 756 in order to make a profit of 5%.
cp=50*4=200
profit %=5%
rotten=40
profit %=(sp-cp)/cp
5=((560(x/12)-200)/200)*100
140x=630
x=4.50