Question

Karim took a loan of Rs. 1500 at the rate of interest same as the number of years. If he paid Rs. 375 as interest at the end of the loan period, find the number of years.

Answer 1

Hint: Here we will apply the simple interest formula. That is:
$\text{Simple interest = }\dfrac{\operatorname{Principal}\times Interest\text{ Rate}\times \text{Time}}{100}$
Here one condition is given which is the rate of interest is the same as the number of years. Apply this condition to form an equation.



Complete step-by-step answer:
According to the question Karim took a loan of Rs. 1500.
Therefore his principal amount is 1500.
It is given in the question that the interest rate is the same as the number of years.

Let us assume that the interest rate is r percent per year.
Therefore the time is also r years.
We know that the simple interest formula is:
$\text{Simple interest = }\dfrac{\operatorname{Principal}\times Interest\text{ Rate}\times \text{Time}}{100}$

Now we can put the values in the above formula. Therefore,
$\text{Simple interest = }\dfrac{1500\times r\times r}{100}=\dfrac{1500{{r}^{2}}}{100}$

According to the question, Karim paid Rs. 375 as interest. Therefore,
$\dfrac{1500{{r}^{2}}}{100}=375$
$\Rightarrow 15{{r}^{2}}=375$

Now we will divide the both sides of the equation by 15.
$\Rightarrow {{r}^{2}}=\dfrac{375}{15}$
$\Rightarrow {{r}^{2}}=25$
$\Rightarrow r={{\left( {{5}^{2}} \right)}^{\dfrac{1}{2}}}$
$\Rightarrow r=5$

Therefore, Karim took the loan for 5 years.

Note: We generally make mistakes while we put the interest rate. We forget to divide by 100 because interest rates are always given in the percent form. Therefore we have to divide the interest rate by 100.