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 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.