Let the sum of money invested be \(P\). Let the rate of simple interest per annum be \(R\%\). Let the time period of investment be \(T\) years. The simple interest (SI) is given by the formula:
\(SI = \frac{PRT}{100}\)
According to the problem, the interest she gets is equal to one-fourth of the sum invested. Therefore,
\(SI = \frac{1}{4}P\)
Also, the time period (in years) of investment is equal to the percentage rate of interest per annum. Therefore,
\(T = R\)
Substituting the value of SI in the simple interest formula, we get:
\(\frac{1}{4}P = \frac{PRT}{100}\)
Since \(P\) is non-zero, we can divide both sides by \(P\):
\(\frac{1}{4} = \frac{RT}{100}\)
Substituting \(T = R\), we get:
\(\frac{1}{4} = \frac{R^2}{100}\)
Solving for \(R\):
\(R^2 = \frac{100}{4} = 25\)
\(R = \sqrt{25} = 5\)
Since \(T = R\), the time period of investment is \(T = 5\) years.
Therefore, Reeta invested the sum of money for 5 years.
Similar Questions
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Important Questions from Simple Interest
How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest ?
Nirav and Mehul borrowed Rs.4000 and Rs.5000 respectively for 2.5 years at the rate of x% per annum. Mehul paid Rs 125 more interest than Nirav. Find x.
The difference between the simple interest received from two banks on Rs. 500 for two years is Rs. 2.50. What is the difference between their rates?
P borrowed an amount from Q at a simple interest of 10% p.a. At the end of the year, P paid back Rs 99000 which was 90% of what she owed. How much money did P borrow?
An amount becomes Rs. 3795 in 3 years and Rs. 4537.50 in \(7 \frac{1}{2}\) years on simple interest. Find the rate of interest per annum.
