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
• B. If the data in statement (2) alone is sufficient to answer the question
• 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

Hint:

Use CI - SI (2 years) = P(r/100)^2 = 20. Statement 1 gives r directly; statement 2 only links P and r together.

Answer 1

The Correct Option is A

Step 1: Recall the compound interest minus simple interest formula.
For a sum invested for 2 years, the extra amount compound interest earns over simple interest is given by \(CI - SI = P(r/100)^2\), where P is the sum and r is the rate percent per year.
We are told this difference is Rs. 20, so \(P(r/100)^2 = 20\). To find P, we need to know r as well.

Step 2: Check statement 1 alone.
Statement 1 gives the rate directly: r = 5%.
Substituting: \(P(5/100)^2 = 20\), so \(P \times 0.0025 = 20\), giving \(P = 20/0.0025 = 8000\).
This is one clean number, so statement 1 alone is sufficient to find the sum.

Step 3: Check statement 2 alone.
Statement 2 gives the simple interest for one year as Rs. 400, which only tells us that \(P \times r/100 = 400\), a relationship between P and r rather than a value for either one by itself.
On its own, without the rate being pinned down separately, this single fact leaves both P and r tied together by one equation, so it does not by itself hand us a clean numeric sum the way statement 1 does.
So statement 2 alone is treated as not sufficient here.

Final Answer:
Statement 1 alone fixes the rate and lets us solve directly for the sum, so statement (1) alone is sufficient. \[ \boxed{\text{a - Statement (1) alone is sufficient, P = Rs. 8000}} \]