Printed price vs. cost price — discount given yet profit earned A shopkeeper offers a 10% discount on the printed (marked) price of a book but still earns a 12% profit on cost. What is the ratio of cost price to printed price of the book?

Introduction / Context:
Retail problems often connect discount off the printed price (which determines selling price) with a profit computed on cost. Converting each statement into equations lets us express cost price (CP) directly as a fraction of printed price (PP).

Given Data / Assumptions:

• Discount on printed price = 10% ⇒ SP = 0.90 × PP.
• Profit on cost = 12% ⇒ SP = 1.12 × CP.
• We need CP : PP.

Concept / Approach:
Since SP is given in two ways, set them equal and isolate CP/PP: 0.90PP = 1.12CP ⇒ CP/PP = 0.90/1.12.

Step-by-Step Solution:
From 0.90PP = 1.12CP, divide both sides by 1.12PP:CP/PP = 0.90 / 1.12 = 0.8035714...Convert to a simple ratio: 0.8035714... = 45/56 ⇒ CP : PP = 45 : 56.

Verification / Alternative check:
Take PP = 56. Then SP = 0.9 × 56 = 50.4. Profit 12% ⇒ CP should be SP/1.12 = 45, giving CP : PP = 45 : 56 (consistent).

Why Other Options Are Wrong:
50 : 61 and 99 : 125 do not produce exactly 10% discount with 12% profit when checked; 'None of these' is false because 45 : 56 fits exactly.

Common Pitfalls:
Applying 12% to the printed price instead of cost, or forgetting that discount is calculated on PP while profit is computed on CP.

Final Answer:
45 : 56