Solve this multiple-choice question and choose the correct option.

Concept & Logic: To find the Cost Price (CP), we need to establish mathematical relationships between CP, Selling Price (SP), and Labelled Price (L) using variables. Step-by-Step Solution: • Target: Find Cost Price (CP). Let Labelled Price = L. • Evaluate Statement I: Richard got a 20% concession on the labelled price. • CP = L - 0.20L = 0.80L. • We have an equation with two unknowns. Not sufficient alone. • Evaluate Statement II: Richard sold the suitcase for ₹ 2000 with a 25% profit on the labelled price. • SP = 2000. Profit = 0.25L. • Since SP = CP + Profit, we have 2000 = CP + 0.25L. • We still have two unknowns (CP and L). Not sufficient alone. • Evaluate Both Together: • Substitute CP = 0.80L (from Statement I) into the equation from Statement II: • 2000 = 0.80L + 0.25L • 2000 = 1.05L \Rightarrow L = (2000/1.05). • Once we find the value of L, we can easily find CP using CP = 0.80L. • Thus, both statements together give a unique value for the cost price. Exam Strategy & Shortcut: You don't need to calculate the final decimal value. Just observe that combining both statements gives you a system of two distinct linear equations with two variables (CP = 0.80L and 2000 = CP + 0.25L), which means it is solvable. Common Pitfall: Misinterpreting "profit on the labelled price" as standard profit on the cost price. You must read the specific base for percentages carefully. Final Answer: Therefore, the correct answer is if the data in both Statements I and II together are necessary to answer the question..

Directions: Each of the questions given below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the question. Read both the statements and Give answer (a) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question; Give answer (b) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question; Give answer (c) if the data either in Statement I or in Statement II alone are sufficient to answer the question; Give answer (d) if the data even in both Statements I and II together are not sufficient to answer the question; Give answer (e) if the data in both Statements I and II together are necessary to answer the question. What was the cost price of the suitcase purchased by Richard? I. Richard got 20% concession on the labelled price. II. Richard sold the suitcase for ₹ 2000 with 25% profit on the labelled price.

if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question;

if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question;

if the data either in Statement I or in Statement II alone are sufficient to answer the question;

if the data even in both Statements I and II together are not sufficient to answer the question;

[Solved] Directions: Each of the questions given below

Answer

Correct Answer: if the data in both Statements I and II together are necessary to answer the question.

Explanation

### Concept & Logic To find the Cost Price (CP), we need to establish mathematical relationships between CP, Selling Price (SP), and Labelled Price (L) using variables. ### Step-by-Step Solution * **Target:** Find Cost Price (CP). Let Labelled Price = $L$. * **Evaluate Statement I:** Richard got a 20% concession on the labelled price. * $\text{CP} = L - 0.20L = 0.80L$. * We have an equation with two unknowns. Not sufficient alone. * **Evaluate Statement II:** Richard sold the suitcase for ₹ 2000 with a 25% profit on the labelled price. * $\text{SP} = 2000$. Profit = $0.25L$. * Since $\text{SP} = \text{CP} + \text{Profit}$, we have $2000 = \text{CP} + 0.25L$. * We still have two unknowns (CP and $L$). Not sufficient alone. * **Evaluate Both Together:** * Substitute $\text{CP} = 0.80L$ (from Statement I) into the equation from Statement II: * $2000 = 0.80L + 0.25L$ * $2000 = 1.05L \Rightarrow L = \frac{2000}{1.05}$. * Once we find the value of $L$, we can easily find CP using $\text{CP} = 0.80L$. * Thus, both statements together give a unique value for the cost price. ### Exam Strategy & Shortcut You don't need to calculate the final decimal value. Just observe that combining both statements gives you a system of two distinct linear equations with two variables ($\text{CP} = 0.80L$ and $2000 = \text{CP} + 0.25L$), which means it is solvable. ### Common Pitfall Misinterpreting "profit on the labelled price" as standard profit on the cost price. You must read the specific base for percentages carefully. ### Final Answer Therefore, the correct answer is **if the data in both Statements I and II together are necessary to answer the question.**.