Ravi bought a scooter at 11/13 of its marked price and sold it at 10% more than the marked price. What was his gain percentage on cost?

Introduction / Context:This problem mixes a purchase below marked price and a sale above marked price. We treat the marked price as a bridge variable to express both the cost price and the selling price, and then compute profit% on cost.

Given Data / Assumptions:

• Let marked price = M.
• Cost price (CP) = (11/13) * M.
• Selling price (SP) = 1.10 * M.

Concept / Approach:Profit% = (SP − CP) / CP * 100. Substituting CP and SP in terms of M allows M to cancel out, leaving a pure percentage.

Step-by-Step Solution:Profit = 1.10M − (11/13)M = M * (1.10 − 0.8461538...) = (33/130)MProfit% = [(33/130)M] / [(11/13)M] * 100 = (33/130) * (13/11) * 100 = 30%

Verification / Alternative check:Pick M = 130 for simplicity: CP = 110; SP = 143; profit = 33; profit% = 33/110 * 100 = 30%.

Why Other Options Are Wrong:24%, 27%, 32%: Do not match the exact ratio obtained from the given fractions.

Common Pitfalls:Calculating profit% on SP; arithmetic slips with fractions or decimal conversion.

Final Answer:30%