Understand the Concept

When a dishonest shopkeeper sells goods using a false weight, the profit percentage is calculated on the actual weight used, not the weight marked on the scale.

$\text{Gain}\% = \frac{\text{Error}}{\text{True Weight}} \times 100$

Set up the Equation

Let the actual weight used be $x$ gm. The shopkeeper gives $x$ gm of goods but charges the customer for $200$ gm. Therefore, the profit is made on $x$ gm.

$\text{Profit} = 200 - x$

Calculate Actual Weight

Given gain percentage is $25\%$. Using the formula for actual weight from false weight: $x = \frac{200}{1 + \frac{25}{100}} = \frac{200}{1.25} = 160 \text{ gm}$

$x = 160 \text{ gm}$