Manufacturing with rejects — Rotomac knows 10% of pens are defective and rejected before packing. The company must deliver 7200 good pens at ₹ 10 each, and it targets 25% overall profit on all pens manufactured (including rejects). What is the manufacturing cost per pen?

Introduction / Context:
This problem couples a reject rate with a profit target on total manufacturing outlay. Because defective pens also cost money to make, the profit percentage must be computed on all units manufactured, not only on units sold (delivered).

Given Data / Assumptions:

• Reject rate = 10% ⇒ good fraction = 90%.
• Good pens required = 7200 ⇒ manufactured pens = 7200 / 0.90 = 8000.
• Selling price per delivered pen = ₹ 10 ⇒ total revenue = 7200 * 10 = ₹ 72,000.
• Target profit = 25% of total manufacturing cost.

Concept / Approach:
Let unit manufacturing cost = c. Total cost = 8000c. Profit condition: Revenue − Cost = 0.25 * Cost. Solve for c using revenue = ₹ 72,000.

Step-by-Step Solution:

Verification / Alternative check:
With c = 7.20, total cost = 8000 * 7.20 = 57,600; profit = 72,000 − 57,600 = 14,400 ⇒ 14,400 / 57,600 = 25%.

Why Other Options Are Wrong:
₹ 6 and ₹ 5.6 understate cost and yield >25% profit; ₹ 8 overshoots cost and yields <25%. ₹ 6.5 is arbitrary here.

Common Pitfalls:
Calculating profit on delivered units only and ignoring the cost of rejects, which inflates the apparent profit.

Final Answer:
Rs. 7.2