Multiple choice

The difference between the compound interest and simple interest for two years on a certain sum at a certain rate of interest is Rs. 64. The compound interest for two years is Rs. 704. The principal is

  1. 800

  2. 1600

  3. 2400

  4. 3200
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For 2 years, CI - SI = P * (r/100)^2 = 64. CI = P * ((1+r/100)^2 - 1) = 704. Dividing these: ((1+r/100)^2 - 1) / (r/100)^2 = 704/64 = 11. Let x = r/100. (1+x)^2 - 1 = 11x^2, so 1 + 2x + x^2 - 1 = 11x^2, 2x = 10x^2, x = 0.2. r = 20%. P * (0.2)^2 = 64, P * 0.04 = 64, P = 1600.

AI explanation

The difference between compound interest and simple interest for two years is given by the formula P * (R/100) squared, so P * (R/100) squared = 64. The compound interest for two years can be expressed as P * (R/100) * (2 + R/100), so P * (R/100) * (2 + R/100) = 704. Dividing the second equation by the first gives (2 + R/100) / (R/100) = 11, which yields R/100 = 0.2. Substituting this back into the first equation gives P * 0.04 = 64, so the principal is 1600.

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