Total cost from a part and a ratio split: The cost of making an article is split between materials, labour, and overheads in the ratio 3 : 4 : 1. If the materials cost ₹ 67.50, find the total manufacturing cost of the article.

Introduction / Context:
When a specific component of a total is given alongside the ratio of all components, you can find the “value per part” and then multiply by total parts. This is a standard proportional allocation technique.

Given Data / Assumptions:

• Materials : Labour : Overheads = 3 : 4 : 1.
• Materials cost = ₹ 67.50 (corresponds to 3 parts).

Concept / Approach:
Compute one-part value as materials cost divided by its ratio part (3). Sum all ratio parts to get total parts, then multiply by one-part value to obtain the total cost.

Step-by-Step Solution:

Verification / Alternative check:
Labour = 4 parts = ₹ 90; Overheads = 1 part = ₹ 22.50; Sum: 67.50 + 90 + 22.50 = 180—checks out.

Why Other Options Are Wrong:
₹ 122.50 and ₹ 200 misapply the parts; ₹ 380 and ₹ 540 are far from the proportional sum.

Common Pitfalls:
Taking ₹ 67.50 as 3% or assuming equal splits; always map actual rupees to the ratio parts given.

Final Answer:
Rs. 180