Multiple choice

The C.I. and S.I. on a sum of money for $2$ years is Rs. $210$ and Rs. $200$ respectively. If the rate of the interest is same the sum and rate will be

  1. $1500, 10 \%$
  2. $1000, 10 \%$
  3. $1200, 8 \%$
  4. $800, 15 \% $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For 2 years, SI = 2Pr = 200, so Pr = 100. CI = P(1+r)^2 - P = 2Pr + Pr^2 = 210. Substituting Pr=100: 200 + 100r = 210, so 100r = 10, r = 0.1 (10%). Then P * 0.1 = 100, so P = 1000.

AI explanation

The difference between compound interest and simple interest for two years is given by the formula Difference = P(r/100)^2, so 210 - 200 = P(r/100)^2, meaning 10 = P(r/100)^2. The formula for simple interest for two years gives 200 = P * r * 2 / 100, which simplifies to P * r = 10000. Substituting Pr = 10000 into the first equation yields 10 = 10000 / (100r), so 1000r = 10000 and r = 10 per cent; substituting r back gives P = 1000.

Keep practicing — related questions