A fruit vendor buys some oranges at the rate of ₹ 5 per orange. He also buys an equal number of bananas at the rate of ₹ 2 per banana. He makes a 20% profit on oranges and a 15% profit on bananas. At the end of the day, all the fruit is sold out. His total profit is 390. Find the number of oranges! purchased.
I want the answer with step by step explanation
I want the answer with step by step explanation
Answers & Comments
Let's assume the vendor buys "x" oranges and "x" bananas.
1. Cost Price (CP) of Oranges:
- Cost of each orange = ₹5
- So, the cost of "x" oranges = 5x
2. Cost Price (CP) of Bananas:
- Cost of each banana = ₹2
- So, the cost of "x" bananas = 2x
Now, let's calculate the profit on oranges and bananas.
3. Profit on Oranges:
- The vendor makes a 20% profit on oranges.
- Profit percentage = 20%
- Profit on each orange = 20% of ₹5 = 0.20 * ₹5 = ₹1
- So, the total profit on "x" oranges = ₹1 * x = ₹x
4. Profit on Bananas:
- The vendor makes a 15% profit on bananas.
- Profit percentage = 15%
- Profit on each banana = 15% of ₹2 = 0.15 * ₹2 = ₹0.30
- So, the total profit on "x" bananas = ₹0.30 * x = ₹0.30x
Now, let's calculate the total profit:
Total Profit = Profit on Oranges + Profit on Bananas
Total Profit = ₹x + ₹0.30x
Total Profit = ₹(1.30x)
Given that the total profit is ₹390:
₹(1.30x) = ₹390
Now, let's solve for "x":
1.30x = 390
Divide both sides by 1.30 to isolate "x":
x = 390 / 1.30
x = 300
So, the vendor purchased 300 oranges.
Therefore, the number of oranges purchased is 300.
Step-by-step explanation:
Let's solve this step by step. Let's assume the fruit vendor bought x oranges and x bananas.
The cost of x oranges would be 5 × x = 5x.
The cost of x bananas would be 2 × x = 2x.
Now, let's calculate the profit on oranges and bananas.
The profit on oranges is 20% of the cost, which is 0.2 × 5x = x.
The profit on bananas is 15% of the cost, which is 0.15 × 2x = 0.3x.
The total profit is the sum of the profit on oranges and bananas, which is x + 0.3x = 1.3x.
According to the given information, the total profit is 390. So, we have the equation:
1.3x = 390
To find the value of x, we divide both sides of the equation by 1.3:
x = 390 / 1.3
Calculating the value of x, we get:
x ≈ 300
Therefore, the fruit vendor purchased approximately 300 oranges.
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