Cost–profit switch: loss to profit swing method: If an item would yield ₹12 more when sold at 8% profit instead of 8% loss, what is the cost price of the furniture?

Introduction / Context:
Changing from an 8% loss to an 8% profit is a total swing of 16 percentage points on the cost price. The rupee change in outcome (₹12) therefore equals 16% of the cost. This “swing method” is a fast technique for many profit–loss questions where two scenarios differ only by percentage on the same base.

Given Data / Assumptions:

• Scenario A: loss = 8% of cost.
• Scenario B: profit = 8% of cost.
• Difference in outcomes between B and A = ₹12.
• Same item, same cost base.

Concept / Approach:
The change from −8% to +8% is a net change of 16% of cost. Therefore 0.16 * Cost = ₹12. Solve for the cost to get a neat integer. No selling price needs to be computed explicitly.

Step-by-Step Solution:

Verification / Alternative check:
At C = 75: 8% loss ⇒ loss = ₹6 ⇒ SP = 69. 8% profit ⇒ profit = ₹6 ⇒ SP = 81. Difference in outcomes = 81 − 69 = ₹12, matching the given.

Why Other Options Are Wrong:
₹72, ₹70, ₹80, ₹60 would yield swings of 11.52, 11.2, 12.8, and 9.6 respectively, not ₹12.

Common Pitfalls:
Applying the 16% swing to selling price rather than cost. The swing is always on the same base as the stated percentages, here the cost price.

Final Answer:
₹ 75