A man has Rs. $10, 000$ to invest. He invests Rs. $4000$ at $5 %$ per annum and Rs. $3500$ at $4 %$ per annum simple interest. At what rate of interest per annum should he invest the remaining amount in order to have an yearly income of Rs. $500$

$12 %$ p.a.

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$6.4 %$ p.a.

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$8 %$ p.a.

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$13.6 %$ p.a.

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Solution

The correct option is B $6.4 %$ p.a.
Let the required rate of interest $= x %$ p.a. Then,
$\frac{4000 \times 5 \times 1}{100} + \frac{3500 \times 4 \times 1}{100} + \frac{(10000 - 4000 - 3500) \times x \times 1}{100} = 500$
$\Rightarrow 200 + 140 + \frac{2500 x}{100} = 500$
$\Rightarrow 25 x = 500 - 340$
$x = \frac{160}{25} = 6.4$ % p.a.

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A man has Rs. 10,000 to invest. He invests Rs. 4000 at 5% per annum and Rs. 3500 at 4% per annum simple interest. At what rate of interest per annum should he invest the remaining amount in order to have an yearly income of Rs. 500

The correct option is B 6.4% p.a.Let the required rate of interest =x% p.a. Then,4000×5×1100+3500×4×1100+(10000−4000−3500)×x×1100=500⇒200+140+2500x100=500 ⇒25x=500−340 x=16025=6.4% p.a.

A man has Rs. $10, 000$ to invest. He invests Rs. $4000$ at $5 %$ per annum and Rs. $3500$ at $4 %$ per annum simple interest. At what rate of interest per annum should he invest the remaining amount in order to have an yearly income of Rs. $500$