Question

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?

• A. 340
• B. 600
• C. 480
• D. 240
• E. 380

Answer 1

The Correct Option is A

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.

1. Let the cost per kg of variety B be \(x\) Rupees.
2. Then, the cost per kg of variety A will be 20% more than B, i.e., \(1.2x\) Rupees.
3. The weights in kg of varieties A and B purchased by Sheela are in the ratio of 5:8.
4. Let the weight of variety A be \(5k\) kg and variety B be \(8k\) kg, where \(k\) is a common multiplier.
5. 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).

1. Simplify Equation 1:

\(6kx + 8kx = 2800\)

\(14kx = 2800\)

Solve for \(kx\):

\(kx = \frac{2800}{14} = 200\) (Equation 2)

1. 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.

1. 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.

1. 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.

Answer 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.