Marked price from selling price with rebate: A shopkeeper offers a 14% rebate on the marked price. If the selling price is ₹645, what is the marked price?

Introduction / Context:
This is an inverse percentage problem. The selling price equals the marked price multiplied by the retention factor after rebate. Recover the marked price by dividing by the retention factor.

Given Data / Assumptions:

• Rebate = 14% ⇒ retention = 86% = 0.86
• Selling Price = ₹645

Concept / Approach:
SP = MP * 0.86 ⇒ MP = SP / 0.86. Ensure clean division and verify by reapplying 14% to check if SP returns to ₹645.

Step-by-Step Solution:
MP = 645 / 0.86 = 750

Verification / Alternative check:
14% of ₹750 is ₹105; subtracting from ₹750 yields ₹645, confirming the result.

Why Other Options Are Wrong:
All other values, when discounted by 14%, do not lead to ₹645.

Common Pitfalls:
Using 14% of SP to back out MP directly; always divide SP by the retention fraction.

Final Answer:
₹ 750