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?

4.6 %

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4.8 %

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5 %

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5.2 %

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Solution

The correct option is C $4.8 %$
Let the amount invested on $4 %$ be Rs. $x$ .
Then remaining amount Rs. $(45000 - x)$ invest at rate $6 %$
Then, according to the question, income from both are equal.
$\Rightarrow \frac{x \times 4 \times 1}{100} = \frac{(45000 - x) \times 6 \times 1}{100}$
$\Rightarrow 2 x = 3 \times 45000 - 3 x$
$\Rightarrow 5 x = 3 \times 45000$
$\Rightarrow x =$ Rs. $27000$
$∴$ Total interest $= \frac{2 \times 27000 \times 4}{100} =$ Rs. $2160$
$∴$ Rate of interest $= \frac{2160 \times 100}{45000} = 4.8 %$ .

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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 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?