Faulty two-pan balance with asymmetric pans — The right pan always reads 200 g heavier than the left. Tika Chand buys by placing goods on the left pan and a 2 kg weight on the right (repeating n times to “weigh” 2n kg), and sells by reversing the order (goods on right, weight on left). He declares prices at his stated cost price per kg. What is his actual overall profit percentage arising from the faulty balance and the buy/sell reversal?

Introduction / Context:
This is a classic “faulty balance” puzzle from profit-and-loss, where the two pans are not equivalent. The right pan effectively adds 200 g of extra pull compared to the left. The merchant cleverly places goods and weights in different pans while buying and selling, creating a hidden gain despite “selling at cost price”. The goal is to compute the true profit percentage caused purely by mismeasurement and pan asymmetry.

Given Data / Assumptions:

• Right pan is effectively 200 g heavier than the left pan.
• Single physical weight available = 2 kg.
• To measure 2n kg, he repeats the 2 kg process n times.
• While buying: goods on left, weight on right. While selling: goods on right, weight on left.
• He “sells at cost price” per nominal kg (declared rate), not per true kg.

Concept / Approach:
Work with one 2 kg operation and then generalize (linearity). Because the right pan is 200 g heavier, the side carrying the right pan requires a smaller true mass to balance when it holds goods, and a larger true mass when it holds the counterweight. Convert each 2 kg nominal transaction into true kilograms to find effective buying cost per true kg and effective selling price per true kg. Profit% = (SP_true − CP_true) / CP_true * 100.

Step-by-Step Solution:

Verification / Alternative check:
Consider n repeats; both received and delivered masses scale proportionally, so the ratio (and hence percentage) remains 22 2/9%. The arithmetic above uses only one 2 kg cycle for clarity.

Why Other Options Are Wrong:
20% and 18 2/11% ignore one of the two biases (buy and sell). “None of these” and 25% do not match the exact ratio 11/9 obtained from simultaneous buying and selling effects.

Common Pitfalls:
Forgetting that the heavier right pan helps the merchant in opposite ways when it holds the goods versus the weight. Another mistake is computing on declared kilograms instead of converting to true kilograms first.

Final Answer:
22 2/9%