Mathematics for FinanceMTP Sep 24 Series IIQuestion 1426 of 512
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The simple interest on a certain sum of money is 125\displaystyle \frac{1}{25} times of principal, the rate of interest when rate of interest and time are equal is

Options

A2%\displaystyle 2\%
B3%\displaystyle 3\%
C4%\displaystyle 4\%
DNone of these
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Correct Answer

✅ Option a — 2%\displaystyle 2\%

All Options:

  • A2%\displaystyle 2\%
  • B3%\displaystyle 3\%
  • C4%\displaystyle 4\%
  • DNone of these

Detailed Solution & Explanation

Let the principal amount be P\displaystyle P. We are given that the Simple Interest (SI\displaystyle SI) on the sum is 125\displaystyle \frac{1}{25} times the principal: SI=125PSI = \frac{1}{25} P Let the rate of interest be r%\displaystyle r\% p.a. and the time period be t\displaystyle t years. We are given that the rate of interest and time are equal: t=rt = r The formula for Simple Interest is: SI=P×r×t100SI = \frac{P \times r \times t}{100} Substituting the values into the formula: 125P=P×r×r100\frac{1}{25} P = \frac{P \times r \times r}{100} 125=r2100\frac{1}{25} = \frac{r^2}{100} r2=10025=4r^2 = \frac{100}{25} = 4 Taking the square root on both sides: r=2r = 2 Thus, the rate of interest is 2%\displaystyle 2\%. Hence, **Option A** is the correct answer.

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