Marked price vs cost when sale at 3/4th MRP gives 25% gain: By selling an article at three-quarters of its marked price, a trader gains 25%. What is the ratio of the marked price to the cost price?

Introduction / Context:
Relate selling price to both MRP and cost via given fractions and gain. With sale at 3/4 of marked price and a 25% profit on cost, equate these two expressions for the same selling price to connect M and C directly as a ratio.

Given Data / Assumptions:

• Marked price = M.
• Selling price S = (3/4)M.
• Profit = 25% ⇒ S = 1.25C.

Concept / Approach:
Set (3/4)M = 1.25C ⇒ M/C = (1.25)/(0.75) = (5/4)/(3/4) = 5/3. Express as a clean ratio M : C = 5 : 3.

Step-by-Step Solution:

Verification / Alternative check:
Let C = 3, then M = 5, S = (3/4)*5 = 3.75; profit = 0.75 = 25% of 3.

Why Other Options Are Wrong:
3:5, 3:4, 4:3, 6:5 contradict the relationship (3/4)M = 1.25C.

Common Pitfalls:
Mixing which percentage applies to M or to C; remember profit is on cost, discount is on marked price.

Final Answer:
5 : 3