Discount given, profit achieved: A shopkeeper sells a book at a 10% discount on its marked price yet makes a 20% profit. What is the ratio of cost price to marked price?

Introduction / Context:
Two simple relations define selling price: SP = 0.90*MP (due to 10% discount) and SP = 1.20*CP (due to 20% profit). Equating them yields CP : MP directly.

Given Data / Assumptions:

• Discount = 10% ⇒ SP = 0.90 * MP
• Profit = 20% ⇒ SP = 1.20 * CP

Concept / Approach:
Equate SP expressions to connect CP and MP, then simplify to a ratio in the lowest terms.

Step-by-Step Solution:

Verification / Alternative check:
Let CP = 3k, MP = 4k ⇒ SP = 0.9*4k = 3.6k, profit = 3.6k − 3k = 0.6k, which is 20% of 3k.

Why Other Options Are Wrong:
Other ratios do not satisfy the simultaneous conditions implied by both discount and profit.

Common Pitfalls:
Mixing the order (MP : CP instead of CP : MP). Always match the requested ratio.

Final Answer:
3 : 4