Multiple choice

Rajat invested a certain sum in Bank Beta at simple interest for a fixed period, while Meera deposited Rs. 20,000 in Bank Gamma also offering simple interest for twice the period for which Rajat invested in Bank Beta. The annual interest rate at Bank Gamma is twice the rate offered by Bank Beta. Had Rajat invested the same amount in Bank Alpha, which offers 6% per annum compounded half-yearly, for one year, the interest earned would have been equal to what he actually earned from Bank Beta. What is the total interest, in rupees, earned by Meera?

  1. 8,000

  2. 4,872

  3. 4,000

  4. 4,850
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Rajat: P, r, t. Interest = Prt/100. Bank Alpha: P(1+6/200)^2 - P = P(1.03^2 - 1) = 0.0609P. So Prt/100 = 0.0609P, rt = 6.09. Meera: 20000 * (2r) * (2t) / 100 = 800 * rt = 800 * 6.09 = 4872.

AI explanation

Bank Alpha compounds 6% per annum half-yearly, meaning a 3% rate applied twice, so Rs. 1000 would yield an interest of 1000 multiplied by 0.03 plus 1030 multiplied by 0.03, which is Rs. 60.90, or a rate of 6.09% for the period. Since this equals Rajat's interest from Bank Beta, Rajat earned 6.09% of his principal, so his effective rate is 6.09%. Meera's principal is Rs. 20,000, her rate is twice Bank Beta's at 12.18%, and her time is twice Rajat's at 2 years. Using the simple interest formula, her interest is 20000 multiplied by 12.18 multiplied by 2 divided by 100, which equals Rs. 4,872.

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