Weighted-average cost with target profit — apples per dozen Ram buys 4 dozen apples at Rs 12 per dozen and 2 dozen at Rs 16 per dozen. If he sells all apples to earn a 20% overall profit, what selling price per dozen should he charge?

Introduction / Context:
When multiple lots are bought at different rates and sold together, compute the total cost and total quantity to get the average cost price. Then scale by the desired profit percentage to obtain the overall selling price per unit (per dozen here).

Given Data / Assumptions:

• Lot A: 4 dozen at Rs 12/dozen ⇒ cost = 48.
• Lot B: 2 dozen at Rs 16/dozen ⇒ cost = 32.
• Total dozens = 6; desired profit = 20% on total cost.

Concept / Approach:
Overall CP = sum of costs. Target SP(total) = CP × 1.20. Then SP per dozen = SP(total)/6.

Step-by-Step Solution:
Total cost = 48 + 32 = 80.Target SP(total) = 80 × 1.20 = 96.SP per dozen = 96 / 6 = Rs 16.00.

Verification / Alternative check:
Average CP per dozen = 80/6 ≈ 13.333. Adding 20% ⇒ 13.333 × 1.20 ≈ 16.00 (matches).

Why Other Options Are Wrong:
Rs 14.40 and Rs 16.80 correspond to ±8% from 16; Rs 19.20 would imply 44% profit; Rs 18.00 overshoots 20% profit.

Common Pitfalls:
Taking a simple mean of 12 and 16 (which ignores quantities) or applying 20% to the higher-priced lot only.

Final Answer:
Rs 16.00