A person invested part of Rs. $4500$ at $4 %$ and the rest at $6 % .$ If his annual income from both are equal, then what is the average rate of interest?

4.6 %

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4.8 %

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5.0 %

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5.2 %

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Solution

The correct option is B $4.8 %$
Let the part invested at $4 %$ by $x$ . Then the part invested at $6 %$ will be $4500 - x$
Annual Income from $x$ $=$ $\frac{x \times 4 \times 1}{100} = \frac{4 x}{100}$
Annual income from $4500 - x$ $=$ $\frac{(4500 - x) \times 6 \times 1}{100}$
Thus, $\frac{4 x}{100} = \frac{(4500 - x) \times 6}{100}$
Cancelling out the $100$ in denominator, we get
$4 x = 6 \times 4500 - 6 x$
$4 x + 6 x = 27000$
$x = 2700$ and $4500 - x = 1800$
Annual income $=$ $2700 \times 0.04 + 1800 \times 0.06$ = $108 + 108 = 216$
Average rate $=$ $\frac{216}{4500} \times 100 = 4.8 %$

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A person invested part of Rs. 4500 at 4% and the rest at 6%. If his annual income from both are equal, then what is the average rate of interest?

A person invested part of Rs. $4500$ at $4 %$ and the rest at $6 % .$ If his annual income from both are equal, then what is the average rate of interest?