Multiple choice

Sagarika divides her savings of 10,000 rupees to invest across two schemes A and B. Scheme A offers an interest rate of 10% per annum, compounded half-yearly, while scheme B offers a simple interest rate of 12% per annum. If at the end of first year, the value of her investment in scheme B exceeds the value of her investment in scheme A by 2,310 rupees, then the total interest, in rupees, earned by Sagarika during the first year of investment is

  1. 1,111

  2. 1,130

  3. 1,000

  4. 1,100
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let A be the amount in scheme A and (10000-A) in scheme B. Interest A = A * ((1.05)^2 - 1) = 0.1025A. Interest B = (10000-A) * 0.12. Given (10000-A)*1.12 - A*1.1025 = 2310. Solving gives 11200 - 2.2225A = 2310, so 2.2225A = 8890, A = 4000. Interest A = 410, Interest B = 720. Total = 1130.

AI explanation

Let the investments in schemes A and B be x and (10000 - x) respectively. The value of investment A after one year is x * (1.05)^2 = 1.1025x, and the value of investment B is (10000 - x) * (1 + 0.12) = 11200 - 1.12x. The difference is 11200 - 1.12x - 1.1025x = 2310, so 2.2225x = 8890, giving x = 4000. The interest earned from scheme A is 4000 * 0.1025 = 410, and the interest from scheme B is 6000 * 0.12 = 720. The total interest earned by Sagarika is 410 + 720 = 1130 rupees.

Keep practicing — related questions