Question

Suppose you have Rs. $12000$ to invest. You have to invest some amount at $10$% and the rest at $15$%. How much should be invested at each rate to yield $12$% on the total amount invested?

Answer 1

Let the time be $1$ year.

For $r=12\%$

$A=P+\left(\frac{P\times r\times t}{100}\right)$

$A=12000+\left(\frac{12000\times 12\times 1}{100}\right)$

$⟹A=Rs.13,440$

Let $Rs.x$ be invested with $12\%$ rate.

Then,

$12000=[x+(\frac{x\times 10\times 1}{100}\left)\right]$$+\left[\right(12000-x)+(\frac{(12000-x)\times 15\times 1}{100}\left)\right]$

Solving for $x$ we get,

$x=7,200$

$⟹12000-7200=4,800$

Hence,$Rs.7200$ is invested at rate $10\%$ and $Rs.4,800$ at rate $15\%$.