Data Sufficiency (Simple Interest): What is the principal sum (in ₹) that earned the interest? Statement A: The total simple interest is ₹9,000 after 9 years. Statement B: The total of principal and simple interest becomes double of the principal after 6 years (at the same simple interest rate).

Introduction / Context:
This is a data sufficiency question in simple interest where we must determine the principal P. Under simple interest, SI = P * r * t / 100 and amount A = P + SI. Statement A provides SI for a given time, which creates only a relation between P and r. Statement B provides a “double in 6 years” condition, which determines the rate r but still does not give P alone. When we combine both, we can compute r from Statement B and then use Statement A to compute P. Therefore, both together are needed.

Given Data / Assumptions:

• SI formula: SI = P * r * t / 100
• Amount: A = P + SI
• Need to find P uniquely
• Statement A: SI = ₹9,000 in 9 years
• Statement B: A = 2P in 6 years

Concept / Approach:
“Double in 6 years” under SI means SI in 6 years equals principal P (since A = P + SI = 2P). That gives a direct equation to compute r. Then use SI from Statement A to compute P.

Step-by-Step Solution:
Statement A only: 9000 = P * r * 9 / 100 Gives only P*r = constant, so P is not unique. Not sufficient. Statement B only: A = 2P in 6 years => SI(6 years) = P P * r * 6 / 100 = P => r = 100/6 = 16 2/3% Rate is found, but P remains unknown. Not sufficient. Using both together: From B: r = 16 2/3% = 50/3% From A: 9000 = P * (50/3) * 9 / 100 (50/3)*9 = 150 9000 = P * 150 / 100 = 1.5P P = 9000 / 1.5 = 6000

Verification / Alternative check:
If P = 6000 and r = 16 2/3%, then SI for 9 years = 6000*(50/3)*9/100 = 9000, correct. For 6 years, SI = 6000, so A = 12000 = 2P, correct.

Why Other Options Are Wrong:
Only A is not enough because rate is unknown. Only B is not enough because principal is unknown. “Either alone” is false. “Neither” is false because together they uniquely determine P. Therefore, both together are required.

Common Pitfalls:
Misinterpreting “double” under SI, forgetting SI in 6 years equals P, or making arithmetic mistakes while handling 16 2/3% (50/3%).

Final Answer:
Both statements are sufficient together (principal comes out to ₹6,000).