A man invested Rs. 5000 at some rate of simple interest and Rs. 4000 at 1 percent higher rate of interest. If the interest in both the cases after 4 years is same, the rate of interest in the former case is

14% p.a.
25% p.a.
3 $6 \frac{1}{4}$ $6\frac{1}{4}$ % p.a.
4 $8 \frac{1}{3}$ $8\frac{1}{3}$ % p.a.

Answer:- 1

Explanation:-

Solution:

Let the rates of interest in the former and latter cases be R% and (R + 1) % p.a.
Then,

\begin{aligned} 5000 \times R \times 4 = 4000 \times (R + 1) \times 4 \\ \Rightarrow \frac{R + 1}{R} = \frac{5000 \times 4}{4000 \times 4} \\ \Rightarrow 1 + \frac{1}{4} \\ \Rightarrow R = 4. \\ Hence, \\ Required rate = 4 % p .a . \end{aligned}

$\eqalign{ & 5000 \times {\text{R}} \times 4 = 4000 \times \left( {{\text{R}} + 1} \right) \times 4 \cr & \Rightarrow \frac{{{\text{R}} + 1}}{{\text{R}}} = \frac{{5000 \times 4}}{{4000 \times 4}} \cr & \Rightarrow 1 + \frac{1}{4} \cr & \Rightarrow {\text{R}} = 4. \cr & {\text{Hence,}} \cr & {\text{Required rate}} = 4\% \,{\text{p}}{\text{.a}}{\text{.}} \cr}$