Marked price and variable selling rates: Selling at 80% of MP results in a 10% loss. What is the profit percentage if the article is sold at 95% of MP?

Introduction / Context:
We connect selling price as a fraction of marked price with profit relative to cost. Determining cost in terms of MP from the first condition lets us compute profit from the second selling rate precisely.

Given Data / Assumptions:

• At SP1 = 0.80 * MP, loss = 10% ⇒ SP1 = 0.90 * CP.
• We seek profit% when SP2 = 0.95 * MP.

Concept / Approach:
From 0.80*MP = 0.90*CP ⇒ CP = (0.80/0.90)*MP = (8/9) * MP. Then profit% at SP2 is (SP2 − CP)/CP * 100% with SP2 = 0.95 * MP.

Step-by-Step Solution:

Verification / Alternative check:
Take MP = 900 ⇒ CP = 800; at 95% of MP, SP2 = 855 ⇒ profit = 55 on 800 ⇒ 6.875%.

Why Other Options Are Wrong:
5%, 5.9%, 12.5% do not match the exact calculation; 6.9% best represents 6.875% to one decimal place.

Common Pitfalls:
Using 0.80*MP = 0.10*CP (misreading loss definition); always tie loss to CP.

Final Answer:
6.9 %