Question

The difference between compound interest and simple interest on a certain sum of money for 2 years is Rs. 20. What is the sum?

Statement 1: Rate of interest is 5%.
Statement 2: Simple interest for one year is Rs. 400.

• A. If the data in statement (1) alone is sufficient to answer the question, but the data in statement (2) alone is not sufficient.
• B. If the data in statement (2) alone is sufficient to answer the question, but the data in statement (1) alone is not sufficient.
• C. If the data in both the statements together are needed to answer the question.
• D. If either statement (1) alone or statement (2) alone is sufficient to answer the question.
• E. If the data in neither statement (1) nor statement (2) is sufficient to answer the question, and more data is needed.

Hint:

Use the identity CI - SI (for 2 years) = P(r/100)^2; you only need the rate to solve for P, not the interest amount.

Answer 1

The Correct Option is A

For 2 years, the difference between compound interest and simple interest on a principal P at rate r% per annum is given by the standard result: Difference = P x (r/100)^2.

Statement 1 tells us the rate is 5%. Plugging in: 20 = P x (5/100)^2 = P x 0.0025, so P = 20/0.0025 = 8000. This gives a single, definite value for the sum, so statement 1 alone is sufficient.

Statement 2 tells us the simple interest for one year is Rs. 400, which means P x r/100 = 400. This is one equation with two unknowns (P and r), so we cannot isolate P without knowing the rate. Statement 2 alone is not sufficient.

Since statement 1 alone gives a unique answer and statement 2 alone does not, the correct choice is (a).