Sheela purchases two varieties of apples – A and B – for a total of Rupees 2800. The weights in kg of A and B purchased by Sheela are in the ratio 5 : 8 but the cost per kg of A is 20% more than that of b. Sheela sells A and B with profits of 15% and 10% respectively. What is the overall profit in Rupees?
- 340
- 600
- 480
- 240
- 380
The Correct Option is A
Approach Solution - 1
Let's solve this problem step-by-step. We need to determine Sheela's overall profit when she buys two varieties of apples and sells them at certain profit percentages.
- Let the cost per kg of variety B be \(x\) Rupees.
- Then, the cost per kg of variety A will be 20% more than B, i.e., \(1.2x\) Rupees.
- The weights in kg of varieties A and B purchased by Sheela are in the ratio of 5:8.
- Let the weight of variety A be \(5k\) kg and variety B be \(8k\) kg, where \(k\) is a common multiplier.
- The total cost of both varieties is 2800 Rupees. Hence, the equation for the total cost is:
\(5k \times 1.2x + 8k \times x = 2800\) (Equation 1).
- Simplify Equation 1:
\(6kx + 8kx = 2800\)
\(14kx = 2800\)
Solve for \(kx\):
\(kx = \frac{2800}{14} = 200\) (Equation 2)
- We find that \(kx = 200\). Using this, calculate individual costs:
The total cost of variety A (5k kg):
\(5k \times 1.2x = 6kx = 6 \times 200 = 1200\) Rupees.
The total cost of variety B (8k kg):
\(8k \times x = 8kx = 8 \times 200 = 1600\) Rupees.
- Sheela sells variety A with a profit of 15% and variety B with a profit of 10%:
Profit on variety A:
\(0.15 \times 1200 = 180\) Rupees.
Profit on variety B:
\(0.10 \times 1600 = 160\) Rupees.
- Calculate the overall profit:
Total profit = Profit on A + Profit on B = \(180 + 160 = 340\) Rupees.
Thus, the overall profit is 340 Rupees. The correct answer is 340.
Approach Solution -2
Let's solve the problem step by step:
Step 1: Determine the weights of A and B.
Let the weights of apples A and B be 5x and 8x respectively, based on their ratio of 5:8.
Step 2: Understand the cost per kg relationship.
Let the cost per kg of apple B be Rs y. Therefore, the cost per kg of apple A will be Rs 1.2y (20% more than B).
Step 3: Formulate the equation based on total cost.
5x * 1.2y + 8x * y = 2800
Therefore, 6xy + 8xy = 2800
So, 14xy = 2800
Thus, xy = 200
Step 4: Calculate the profit Sheela earns from each type of apple.
Sheela earns a 15% profit on A and a 10% profit on B. Calculating the selling prices:
- Selling price of A = 5x * 1.2y * 1.15
- Selling price of B = 8x * y * 1.1
Add the selling prices to find the total selling price:
Total selling price = 5x * 1.2y * 1.15 + 8x * y * 1.1
Total selling price = 5x * 1.38y + 8x * 1.1y
Total selling price = 6.9xy + 8.8xy
Total selling price = 15.7xy
Given xy = 200, the total selling price is 15.7 * 200 = 3140.
Step 5: Determine the overall profit.
Overall profit = Total selling price - Total cost price
Overall profit = 3140 - 2800 = 340
Conclusion: The overall profit is Rs 340.
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