A fruit vendor buys 300 Apple at rupees 50 per dozen the vendors old 200 of them at rupees 60 per dozen at what rate per Apple should the vendors sell the remaining apples to make an overall profit of 12%
I don't know , please tell it to me
you want income = cost * 1.12, so
200 * 60/12 + 100 * x/12 = 300 * 50/12 * 1.12
solve for x, the price per dozen.
To find the rate per Apple at which the vendor should sell the remaining apples to make an overall profit of 12%, we need to calculate the total cost and the total selling price of the apples.
Let's break down the information given:
1. The vendor buys 300 apples at rupees 50 per dozen. Therefore, the cost per apple is: (50 rupees / 12 apples) = 4.17 rupees per apple.
2. The vendor sells 200 apples at rupees 60 per dozen. Therefore, the selling price per apple is: (60 rupees / 12 apples) = 5 rupees per apple.
Now, let's calculate the total cost and selling price:
Total cost = (Total number of apples bought) * (Cost per apple)
= (300 apples) * (4.17 rupees/apple) = 1251 rupees
Total selling price = [(Number of apples sold) * (Selling price per apple)] + [(Number of remaining apples) * (Selling price per apple)]
We know that the number of remaining apples is: (Total number of apples bought - Number of apples sold)
= (300 apples - 200 apples) = 100 apples.
We need to find the selling price per apple when the overall profit is 12%. To achieve this, the selling price should be 112% of the cost price.
112% of the cost price per apple = (112/100) * (4.17 rupees/apple) = 4.67 rupees per apple.
Now, let's substitute these values into the equation for the total selling price:
Total selling price = [(200 apples) * (5 rupees/apple)] + [(100 apples) * (4.67 rupees/apple)]
= 1000 rupees + 467 rupees
= 1467 rupees
To get the desired profit of 12%, the selling price should be 12% more than the cost price.
Desired selling price = (112/100) * (Total cost)
= (112/100) * (1251 rupees)
= 1401.12 rupees
Since the vendor has already sold some apples for 1000 rupees (as calculated earlier), the selling price of the remaining apples should be:
Remaining selling price = Desired selling price - Total selling price
= 1401.12 rupees - 1467 rupees
= -65.88 rupees
Based on this calculation, it appears that the vendor cannot achieve an overall profit of 12% by selling the remaining apples. They would incur a loss of 65.88 rupees.