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# A man has Rs10,000 invested. He invests Rs4000 at 5% and Rs3500 at 4%. In order to have a yearly income of Rs500 he must invest the remainder at:$\left(a\right)6\%$$\left(b\right)6.1\%$$\left(c\right)6.2\%$$\left(d\right)6.3\%$$\left(e\right)6.4\%$

Last updated date: 13th Jul 2024
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Hint: This is a question related to interest generated on some principal. We are given the total amount invested and we are also given the amount of revenue that the person should be able to generate. So first of all we will calculate the revenue generated so far and then we will apply the formula for simple interest to calculate the rate at which the amount should be invested at.

Complete step-by-step solution:
We’ll do this step by step. First, see that the man has invested the total amount of:
$4000+3500=Rs7500$
So, the remaining amount becomes $10000-7500=2500$.
Now, we will calculate the revenue generated one by one:
Rs4000 is invested at 5%, so the revenue generated from this is equal to:
$4000\times \dfrac{5}{100}=200$
Rs3500 is invested at 4%, so the revenue generated from that amount will be:
$3500\times \dfrac{4}{100}=140$
Total revenue generated till now is equal to the sum of these:
$200+140=340$
Total revenue that should be generated is Rs500.
So, the remaining revenue to be generated will be:
$500-340=Rs160$
Now, the remaining amount i.e. Rs2500 is supposed to raise the revenue of Rs160. So, to calculate the rate at which this should be invested to generate the given revenue, we simply use the following formula:
$Interest=Principal\times Rate\times Time$
Here, Principal is Rs2500. The Interest is Rs160. And it is annual so the time is 1 year. Plugging in these values, we get:
$160=2500\times r\times 1$
$r=\dfrac{160}{2500}=0.064$
Converting the same into percentage we get:
$r=0.064\times 100=6.4\%$
Hence, option $\left(e\right)6.4\%$ is correct.

Note: You should remember that multiplying a fraction or decimal with 100 will give the percentage. So do not forget to fraction or decimal multiply by 100 otherwise it would lead to an incorrect solution. Also, we need to be aware about all the formulae of interest and terms such as principle, rate and so on.