Simple interest on Rs. 500 for 4 years at 6.25% per annum is equal to the simple interest on Rs. 400 at 5% per annum for a certain period of time. The period of time is = ?

14 years
25 years
3 $6 \frac{1}{4}$ $6\frac{1}{4}$ years
4 $8 \frac{2}{3}$ $8\frac{2}{3}$ years

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Let the required time \\ =  t years \\ According to the question, \\ \Leftrightarrow \frac{500 \times 4 \times 6.25}{100} = \frac{400 \times 5 \times t}{100} \\ \Leftrightarrow 5 \times 4 \times 625 = 400 \times 5 \times t \\ \Leftrightarrow t  = \frac{625}{100} = \frac{25}{4} \\ \Leftrightarrow t = \frac{1}{4} years \end{aligned}

$\eqalign{ & {\text{Let the required time }} \cr & {\text{ = t years}} \cr & {\text{According to the question,}} \cr & \Leftrightarrow \frac{{500 \times 4 \times 6.25}}{{100}} = \frac{{400 \times 5 \times {\text{t}}}}{{100}} \cr & \Leftrightarrow 5 \times 4 \times 625 = 400 \times 5 \times {\text{t}} \cr & \Leftrightarrow {\text{t = }}\frac{{625}}{{100}} = \frac{{25}}{4} \cr & \Leftrightarrow {\text{t}} = \frac{1}{4}{\text{years}} \cr}$