A vendor sells 36 oranges and incurs a loss equal to the selling price of 4 oranges. Compute the loss percentage.

Introduction:Loss or gain expressed in terms of the selling price of some quantity is a classic framing. Turning it into algebra using per-unit selling price and comparing total selling price with total cost gives the required percentage.

Given Data / Assumptions:

• Let s be the selling price per orange.
• Total oranges sold = 36.
• Loss amount = selling price of 4 oranges = 4s.

Concept / Approach:Total SP = 36s. Since there is a loss of 4s, total CP must be SP + loss = 36s + 4s = 40s. Loss percentage is loss divided by cost times 100.

Step-by-Step Solution:Total SP = 36sLoss = 4sTotal CP = 36s + 4s = 40sLoss% = 4s / 40s * 100 = 10%

Verification / Alternative check:Assume s = Rs 10. Then SP = 360, loss = 40, CP = 400, giving 40/400 * 100 = 10%, consistent.

Why Other Options Are Wrong:

• 12.5% and 11 1/9%: incorrect ratios from misplacing the base.
• None of these: incorrect because 10% is correct.

Common Pitfalls:

• Computing percentage on selling price instead of on cost price.
• Interpreting the loss as 4 oranges out of 36 without converting rupee values.

Final Answer:10%