A fruit seller claims to sell at cost price but uses a 450 g weight in place of 500 g. Find his percentage profit.

Introduction:
False-weight problems are classic profit tricks. Even if the price tag equals the cost price per “kilogram,” giving less than a kilogram increases the effective selling price per true kilogram, creating a hidden margin. We compute the effective gain when 450 g is passed off as 500 g at the stated cost price.

Given Data / Assumptions:

• Claimed selling price = cost price per 500 g unit (honest label)
• Actual quantity delivered per “500 g” sale = 450 g
• Let CP per kg = C rupees (unknown, cancels)

Concept / Approach:
If the seller charges for 500 g at the cost rate, the nominal charge for 500 g = 0.5 * C. But the buyer receives only 0.45 kg, so the revenue per true kg equals (0.5 * C) / 0.45. Compare this with the true cost per kg C to find the profit percentage.

Step-by-Step Solution:
Effective SP per true kg = (0.5 * C) / 0.45 = (10/9) * C ≈ 1.111... * CProfit% = [(Effective SP − C) / C] * 100 = (1.111... − 1) * 100 = 11.111...%11.111...% = 11 1/9 %

Verification / Alternative check:
On 0.45 kg: charged = 0.5 * C; cost to seller = 0.45 * C; gain = 0.05 * C; gain% on cost = (0.05/0.45)*100 = 11.111...%.

Why Other Options Are Wrong:
10%, 12%, 12 2/9%: These do not match 0.05/0.45 exactly.

Common Pitfalls:
Using 500/450 directly as profit%; forgetting to compute profit relative to the true cost per kg; mixing per-kg and per-500 g bases.

Final Answer:
11 1/9 %