Commission and advertised price with profit: A shopkeeper allows 23% commission on his advertised price and still makes a profit of 10%. If his profit on one item is ₹56, what is the advertised price?

Introduction / Context:
The seller gives an agent a commission on the advertised price (AP) yet achieves a fixed profit percent on cost. Profit in rupees allows finding the cost price first, then the necessary advertised price using the commission relationship.

Given Data / Assumptions:

• Commission = 23% of Advertised Price (A).
• Seller’s profit% = 10% ⇒ Profit (₹) = 0.10 * CP = ₹56.
• So CP = 56 / 0.10 = ₹560.

Concept / Approach:
Selling price to the seller is the advertised price minus commission: SP = A − 0.23A = 0.77A. Also SP = CP + Profit = 560 + 56 = ₹616. Equate to solve for A.

Step-by-Step Solution:

Verification / Alternative check:
Commission = 0.23*800 = 184. Net to seller = 616. Profit = 616 − 560 = 56, which is exactly 10% of 560.

Why Other Options Are Wrong:
820, 780, 790 do not satisfy 0.77A = 616; 800 is the only correct value.

Common Pitfalls:
Taking commission on SP or CP instead of the advertised price as specified.

Final Answer:
800