Multiple choice

A certain sum of money amounts to Rs. 1008 in 2 years and to Rs. 1164 in $3\, \displaystyle \frac{1}{2}$ years. Find the rate of interest.

  1. 11%

  2. 12%

  3. 13%

  4. 14%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Amount in 2 years = 1008. Amount in 3.5 years = 1164. Interest for 1.5 years = 1164 - 1008 = 156. Interest for 1 year = 156 / 1.5 = 104. Interest for 2 years = 208. Principal = 1008 - 208 = 800. Rate = (Interest * 100) / (Principal * Time) = (104 * 100) / (800 * 1) = 13%.

AI explanation

The simple interest for the extra 1.5 years is the difference between the two amounts, which is 1164 minus 1008, giving Rs. 156. The interest for 2 years is 156 times 2 divided by 1.5, which equals Rs. 208, meaning the principal is 1008 minus 208, giving Rs. 800. Using the Simple Interest formula, the rate is 100 times 208 divided by 800 times 2, which results in 13 percent.

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