Unitary method (direct proportion): If 20 articles cost ₹ 90, what is the cost of 9 articles?

Introduction / Context:
The unitary method solves direct proportion questions by first finding the cost per single item, and then scaling to the desired number of items. Prices are assumed linear with quantity here (no bulk discounts indicated).

Given Data / Assumptions:

• 20 articles cost ₹ 90.
• Find the cost of 9 identical articles.

Concept / Approach:
Cost per article = total cost / total articles. Then multiply by the required quantity (9).

Step-by-Step Solution:

Verification / Alternative check:
Proportion check: 9/20 of ₹ 90 = ₹ (9 × 90 / 20) = ₹ 40.5, agreeing with the unitary computation.

Why Other Options Are Wrong:

• ₹ 45: Would correspond to 10 articles at ₹ 4.50 each, not 9.
• ₹ 4.50: This is the per-article cost, not the cost for 9 articles.
• None of these: Not applicable because ₹ 40.50 is attainable and correct.

Common Pitfalls:
Dividing 20 by 90 instead of 90 by 20, or forgetting to multiply by 9 at the end. Keep the proportionality direction consistent: more articles cost more.

Final Answer: