Mixing bananas of two price types to hit a target price: How many bananas at 5 for ₹ 1.20 (₹ 0.24 each) should be mixed with 300 bananas at 6 for ₹ 2.10 (₹ 0.35 each) so that the mixture is worth ₹ 3.60 per dozen (₹ 0.30 each)?

Introduction / Context: This is a weighted-average price problem. The target price per unit dictates the total value for the combined quantity. Let the number of cheaper bananas be x, write total value and total items, and enforce the target average price per banana (₹ 0.30).

Given Data / Assumptions:

• Cheaper: ₹ 0.24 each; quantity = x.
• Costlier: ₹ 0.35 each; quantity = 300.
• Target average = ₹ 0.30 each.

Concept / Approach: (0.24x + 0.35*300) / (x + 300) = 0.30. Solve for x to determine how many cheaper bananas to add.

Step-by-Step Solution:

Verification / Alternative check: Total items = 550; total value = 0.24*250 + 0.35*300 = 60 + 105 = ₹ 165; 165/550 = ₹ 0.30 each ⇒ ₹ 3.60 per dozen.

Why Other Options Are Wrong: Any other x changes the average above or below ₹ 0.30; the equation balances only at x = 250.

Common Pitfalls: Mixing “per dozen” with “per banana” inconsistently; always convert to a per-unit basis for equations.

Final Answer: 250