Question

A person invested part of Rs. 45000 at 4% and the rest at 6%. If his annual income from both is equal, then what is the average rate of interest?
A. 4.6%
B. 4.8%
C. 5%
D. 5.2%

Answer 1

Hint: Here we will proceed by calculating the investment and interest rate. After that with investment and interest rate we can easily calculate the average rate of interest.

Complete step-by-step answer:
In this question, it is given that a man invested Rs. 45000 at 4% and the rest 45000-P at 6%.
Let the investment be P.
Now, we can say P was invested at 4% and 6%
Now interest from P = $P\times 4\times {\displaystyle \frac{1}{100}}$$=0.04P$
Interest from 45000-P = $\left(45000-P\right)\times 6\times {\displaystyle \frac{1}{100}}=2700-0.06P$
Now, as we know that his annual income from both is same then,
$$\begin{gathered} \Rightarrow 0.04P=2700-0.06P \\ \Rightarrow 0.1P=2700\text{ (adding 0}\text{.06)} \\ \Rightarrow P=27000\text{ (multiplying by 0}\text{.1) } \end{gathered}$$
Therefore, 27000 was invested at 4%
Also we can say that,
45000-27000 = 18000 invested at 6%
Now, finding total interest,
$$\begin{gathered} =27000\times 4\times {\displaystyle \frac{1}{100}}+18000\times 6\times {\displaystyle \frac{1}{100}} \\ =1080+1080 \\ =2160 \end{gathered}$$
To find the average interest (let it be ‘R’),
$$\begin{gathered} \Rightarrow 2160=45000\times R\times {\displaystyle \frac{1}{100}} \\ \Rightarrow R=4.8\mathrm{\%} \end{gathered}$$
Therefore, average interest = 4.8% (B) is the correct option.

Note: Whenever we come up with this type of question, one must know that it is important to calculate annual income from both the interest rates. Then it is important to find out the total interest rate. By total interest rate we will calculate the average rate of interest thus we will get our required answer.