Directions: Each of the following questions consists of a question followed by three statements I, II and III. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. What was the cost price of the watch? I. The shopkeeper labelled the price of the watch 20% above the cost price. II. After allowing a discount of 15% on the labelled price, the shopkeeper charges ₹ 408 for the watch. III. Had there been no discount, the shopkeeper would have earned 20% profit.

### Concept & Logic To find the Cost Price (CP), we need an absolute value and a sequence of percentage relationships connecting that absolute value to the CP. The relationship between Marked Price (MP), Selling Price (SP), and CP is key. ### Step-by-Step Solution * Statement II provides an absolute value: Selling Price (SP) = ₹ 408, and relates it to the Labelled Price (MP) with a $15\%$ discount. So, SP = $0.85 \times \text{MP}$. Statement II is essential because it is the only one with an absolute monetary value. * Statement I states MP is $20\%$ above CP, meaning $\text{MP} = 1.2 \times \text{CP}$. * Statement III states that with no discount (meaning $\text{SP} = \text{MP}$), the profit is $20\%$. This also means $\text{MP} = 1.2 \times \text{CP}$. * Notice that statements I and III convey the exact same mathematical relationship between the Marked Price and Cost Price. * To find CP, we can use statement II to find MP, and then use either statement I or statement III to find CP from MP. * Thus, we need statement II and either statement I or III. ### Exam Strategy & Shortcut Identify redundant statements. Statements I and III are logically identical. Therefore, any combination that works with I will also work with III. This points directly to the option "II, and either I or III". ### Common Pitfall Choosing "I and II only" because they are sufficient, while failing to realize that statement III can perfectly substitute for statement I. ### Final Answer Therefore, the correct answer is **II, and either I or III**.