Multiple choice

Directions: In this problem, a question is followed by two statements labelled A and B. Read the statements carefully and decide which of the given statements is/are sufficient to answer the question. Choose the correct option accordingly. In how many years will a certain amount 'a' increase by Rs. 205 at a rate of x% p.a. compound interest? (A) x = 5% (B) a is Rs. 205.

  1. Statement (A) alone is sufficient but statement (B) alone is not sufficient.

  2. Statement (B) alone is sufficient but statement (A) alone is not sufficient.

  3. Both statements (A) and (B) together are sufficient but neither of them alone is sufficient.

  4. Both statements (A) and (B) are sufficient independently.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Compound interest formula: A = P(1 + r/100)^n. We need to find n. We have P = a, A = a + 205, r = x. Statement A gives r=5. Statement B gives P=205. Neither is sufficient alone because we have two variables (a and n) or need both P and r to solve for n.

AI explanation

To find the time for an amount to increase by a specific value under compound interest, we need both the principal and the rate of interest. Statement A provides the rate x = 5% but lacks the principal, while statement B provides the principal a = Rs. 205 but lacks the rate. Using both together in the compound interest formula allows us to solve for the time, so both statements A and B together are sufficient but neither statement alone is sufficient.

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