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Consider the given question and decide which of the following statement(s) is/are sufficient to answer the question. X took a loan from Y on compound interest. Find the rate per annum. Statements: 1. After 3 years, X paid Rs. 500 as interest. 2. After 3 years, X paid Rs. 1,500 to clear his loan with Y.

Consider the given question and decide which of the following statement(s) is/are sufficient to answer the question. X took a loan from Y on compound interest. Find the rate per annum. Statements: 1. After 3 years, X paid Rs. 500 as interest. 2. After 3 years, X paid Rs. 1,500 to clear his loan with Y. Correct Answer Both 1 and 2 together are sufficient to answer the question.

X took a loan from Y on compound interest.

Statement 1: 

After 3 years, X paid Rs. 500 as interest.

Interest = Rs. 500

⇒ A = P(1 + r/100)t, 

But principal amount is not given so we cannot find the rate.

Statement 2: 

After 3 years, X paid Rs. 1,500 to clear his loan.

Amount = Rs. 1500

⇒ A = P(1 + r/100)t, 

But neither principal amount nor interest is given, so we cannot find the rate.

Statement 1 and 2 together:

Amount = Rs. 1500, interest = Rs. 500

⇒ Principal = Rs. 1000

Hence, rate can be calculated using both the statements together.

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