Price-tag versus transaction rates: the CP:MP ratio is 2:3. The ratio of profit percentage to discount percentage is 3:2. Assuming the same selling price links both expressions, find the discount percentage.

Introduction:
Here, the selling price (SP) simultaneously equals CP increased by profit% and MP reduced by discount%. Equating these two expressions and using the given ratios yields the required discount%.

Given Data / Assumptions:

• CP:MP = 2:3 ⇒ CP = 2k, MP = 3k.
• Profit% : Discount% = 3:2 ⇒ let profit% = 3t, discount% = 2t.

Concept / Approach:
SP = CP * (1 + profit%) = MP * (1 − discount%). Solve for t and compute discount% = 2t.

Step-by-Step Solution:
2k * (1 + 3t/100) = 3k * (1 − 2t/100)2 + 0.06t = 3 − 0.06t0.12t = 1 ⇒ t = 8.333... ⇒ discount% = 2t = 16.666...%

Verification / Alternative check:
Plugging back gives identical SP from both sides, confirming consistency.

Why Other Options Are Wrong:

• 20% / 25% / 33.33%: stem from algebra slips or swapping bases.

Common Pitfalls:

• Applying the 3:2 ratio to rupee profits/discounts instead of percentages.

Final Answer:
16.66 %