UPSC CDS 2 2020 Math Paper

Concept:When a shopkeeper sells at cost price but uses a faulty balance that shows a higher weight than the actual weight given, the profit arises from the difference between the weight charged and the weight actually supplied.Explanation:The balance reads $1000$ gm, but the shopkeeper actually gives only $800$ gm.The customer pays for $1000$ gm, while the shopkeeper loses only $800$ gm from stock.Let the cost price (CP) of $1$ gm be $\text{Rs.}1$.Then, the effective CP for the shopkeeper is $\text{Rs.}800$ (cost of the goods given).The effective selling price (SP) is $\text{Rs.}1000$ (amount received from customer).$\text{Profit} = \text{SP} - \text{CP} = \text{Rs.}1000 - \text{Rs.}800 = \text{Rs.}200$.Profit percentage = $\frac{\text{Profit}}{\text{Effective CP}} \times 100 = \frac{200}{800} \times 100 = 25\%$.Alternatively, using the formula for faulty weight: Profit % = $\frac{\text{Stated weight} - \text{Actual weight}}{\text{Actual weight}} \times 100 = \frac{1000 - 800}{800} \times 100 = 25\%$.Thus, the actual profit percentage is $25\%$.Answer:$25\%$ (Option B)