Multiple choice

A sum of money invested at simple interest becomes Rs. $306$ at the end of $5$ years. If the interest is $\left (\displaystyle \frac{9}{25}\right)^{ th}$ part of the principal, what is the rate of interest per annum ?

  1. $5\dfrac{1}{5} \%$ p.a.
  2. $7\dfrac{1}{5} \%$ p.a.
  3. $9\dfrac{1}{5} \%$ p.a.
  4. $11\dfrac{1}{5} \%$ p.a.
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B Correct answer
Explanation

Interest I = (9/25)P. Amount A = P + I = P + 0.36P = 1.36P. 1.36P = 306, so P = 225. Interest I = 306 - 225 = 81. I = (P*R*T)/100 => 81 = (225*R*5)/100. 81 = 11.25R, R = 7.2%. 7.2% is 7 1/5%.

AI explanation

Let the principal be P, so the interest is (9/25)P and the amount is P plus (9/25)P, which equals 34/25 of P. Since the amount is 306, we solve for P to get P equals 306 multiplied by 25 divided by 34, resulting in a principal of 225. Using the simple interest formula, Rate equals (Interest times 100) divided by (Principal times Time), we substitute the values to get R equals (81 times 100) divided by (225 times 5). This simplifies to 8100 divided by 1125, which equals 7.2% or 7 1/5% per annum.

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