Profit and Loss – Profit% from 12:9 CP:SP relation and discount tied to profit: The cost price (CP) of 12 oranges equals the selling price (SP) of 9 oranges. Also, the discount on 10 oranges equals the profit on 5 oranges. What is the percentage-point difference between the profit percentage and the discount percentage?

Introduction / Context:
We are given two independent relations: one linking CP and SP via a 12:9 equivalence, and another tying discount (in money) on 10 units to profit (in money) on 5 units. The goal is the difference in percentage points between profit% and discount% (both computed with their appropriate bases).

Given Data / Assumptions:

• 12 * CP_per_orange = 9 * SP_per_orange
• 10 * (MP − SP) = 5 * (SP − CP)

Concept / Approach:
From the first relation, SP = (4/3) * CP, giving profit% = (SP − CP) / CP * 100 = (1/3) * 100 = 33.33...%. For the second, 10(MP − SP) = 5(SP − CP) ⇒ 2(MP − SP) = SP − CP. Substitute SP − CP = CP/3 and solve for the discount% = (MP − SP) / MP * 100.

Step-by-Step Solution:
From 12CP = 9SP ⇒ SP = 4/3 CP ⇒ Profit% = (1/3)*100 = 33.33...%2(MP − SP) = SP − CP = CP/3 ⇒ MP − SP = CP/6But 3SP − CP = 2MP ⇒ with SP = 4/3 CP gives MP = (3SP − CP)/2 = (4CP − CP)/2 = 3CP/2Discount% = (MP − SP) / MP * 100 = (CP/6) / (3CP/2) * 100 = (1/6) * (2/3) * 100 = 11.11...%Difference = 33.33... − 11.11... = 22.22 percentage points

Verification / Alternative check:
Pick CP = 3, then SP = 4, MP = 4.5. Profit% = 1/3 ≈ 33.33%; Discount% = 0.5/4.5 ≈ 11.11%; difference ≈ 22.22.

Why Other Options Are Wrong:
20 and 15 are too low; 16.66 is not the exact difference; 25 overstates the gap.

Common Pitfalls:
Confusing money-equality (profit vs discount) with percentage equality; each uses a different base.

Final Answer:
22.22