Multiple choice

A and B invested Rs. 24,000 each. A invested at simple interest at the rate of 9% per annum and B invested at compound interest at the rate of x% per annum. If both A and B invested the money for two years, what could be the possible value of x given that B got at least Rs. 3420 more interest than A? (i) 15% (ii) 14% (iii) 18% (iv) 12% (v) 10%

  1. Only (ii), (iv) and (v)

  2. Only (ii) and (iv)

  3. Only (i) and (iii)

  4. Only (i), (iii) and (v)

  5. All of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A's interest = 24000 * 0.09 * 2 = 4320. B's interest = 24000 * ((1 + x/100)^2 - 1). We need B - A >= 3420, so B >= 7740. (1 + x/100)^2 - 1 >= 7740 / 24000 = 0.3225. (1 + x/100)^2 >= 1.3225. 1 + x/100 >= 1.15. x >= 15. Options (i) 15% and (iii) 18% satisfy this.

AI explanation

Using the simple interest formula for A, the interest is (24000 times 9 times 2) divided by 100, which equals 4320 rupees. For B to get at least 3420 rupees more, the compound interest on 24000 for two years must be at least 7740 rupees, making the minimum required amount 31740 rupees. Testing the given rates, 15% yields an amount of 31740 rupees and 18% yields an amount of 33379.20 rupees, both of which satisfy the condition, while the lower rates fail to produce enough interest. Therefore, only 15% and 18% are the possible values for x.

Keep practicing — related questions