Loss-to-cost recovery: Niraj sells an article for ₹ 9,549 incurring a loss of 55%. Determine the original cost price of the article.

Introduction / Context:When loss% is known with the selling price, the cost price can be found by dividing by the remaining percentage factor because SP = (1 − loss%) * CP.

Given Data / Assumptions:

• SP = ₹ 9,549.
• Loss = 55% ⇒ SP = 0.45 * CP.

Concept / Approach:Rearrange SP = 0.45 * CP to CP = SP / 0.45 and compute directly.

Step-by-Step Solution:CP = 9,549 / 0.45 = ₹ 21,220

Verification / Alternative check:Check: 45% of 21,220 is 9,549; hence SP at 55% loss equals 21,220 − 11,671 = 9,549, verifying the relationship (or directly 0.45 * 21,220 = 9,549).

Why Other Options Are Wrong:

• ₹ 27,700 / ₹ 25,600 / ₹ 29,000: result from dividing by the wrong factor or arithmetic slips.

Common Pitfalls:

• Treating 55% of SP rather than of CP as the loss base.

Final Answer:₹ 21,220