A person deposits Rs. 500 in 4 years and Rs. 600 for 3 years at the same rate of simple interest in a bank. Altogether he received Rs. 190 as interest. The rate of simple interest per annum was = ?

Solution(By Examveda Team)

Let rate of interest = R%
According to the question,
$$\eqalign{ & \frac{{500 \times 4 \times {\text{R}}}}{{100}} + \frac{{600 \times 3 \times {\text{R}}}}{{100}} = 190 \cr & \Rightarrow 20{\text{R + 18R = 190}} \cr & \Rightarrow 38{\text{R = 190}} \cr & \Rightarrow {\text{R = 5% }} \cr} $$
Hence required rate % = 5%

Alternate
Note : In such type of questions to save your valuable time follow the given below method.
Let rate of interest = 1%
$$\eqalign{ & {\text{Case (I): Interest (}}{{\text{I}}_1}{\text{)}} \cr & {\text{ = }}\frac{{500 \times 4 \times 1}}{{100}} \cr & = 20 \cr & {\text{Case (II): Interest (}}{{\text{I}}_2}{\text{)}} \cr & {\text{ = }}\frac{{{\text{600}} \times 3 \times 1}}{{100}} \cr & = 18 \cr} $$
According to the question,

Interest	Rate %
38	1
↓×5	↓×5
190	5%

Hence required rate % = 5%