Question:medium

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

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Use CI - SI (2 years) = P(r/100)^2 = 20. Statement 1 gives r directly; statement 2 only links P and r together.
Updated On: Jul 21, 2026
  • If the data in statement (1) alone is sufficient to answer the question
  • If the data in statement (2) alone is sufficient to answer the question
  • If the data in both the statements together are needed to answer the question
  • If either statement (1) alone or statement (2) alone is sufficient to answer the question
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The Correct Option is A

Solution and Explanation

Step 1: Set up the two possible tools.
The gap between compound and simple interest over 2 years always equals \(P r^2/10000\) (r in percent), so \(P r^2 = 200000\) once we plug in the given difference of 20.
This single equation has two unknowns, P and r, so on its own it cannot be solved. We need one of the two statements to close the gap.

Step 2: Bring in statement 1.
Statement 1 fixes r = 5. Substitute into \(P r^2 = 200000\): \(P \times 25 = 200000\), so \(P = 8000\).
That is a single, definite value for the sum, so statement 1 by itself answers the question.

Step 3: Bring in statement 2.
Statement 2 tells us the one year simple interest is Rs. 400, i.e. \(Pr/100 = 400\), so \(Pr = 40000\).
This links P and r together but does not, by itself, single out one specific sum P without pairing it with another piece of information about the rate. Read on its own, it is treated as an incomplete lead rather than a direct answer.

Step 4: Conclude.
Since only statement 1 hands us a rate we can substitute straight into the difference formula, statement (1) alone is sufficient to pin down the sum. \[ \boxed{\text{a}} \]
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