Question

Divide $Rs.3,600$ into two parts such that if one part be lent at $9\%$ per annum and the other at $10$ per annum, the total annual income is $Rs.333$.

Answer 1

Let $Rs.3600$ be divided into two parts $x$ and $y$ respectively.

$x+y=3600$

$y=3600-x$

As we know that,

$S.I.=\frac{P\times R\times t}{100}$

Now,

For $Rs.x$,

Rate of interest $=9\%$ per annum

$t=1$

$S.I.=\frac{x\times 9\times 1}{100}$

For $Rs.y$,

Rate of interest $=10\%$ per annum

$t=1$

$S.I.=\frac{y\times 10\times 1}{100}$

$\Rightarrow S.I.=\frac{(3600-x)\times 10}{100}$

Now, according to the question-

$\frac{9x}{100}+\frac{10(3600-x)}{100}=333$

$\Rightarrow 9x+36000-10x=33300$

$\Rightarrow x=36000-33300=2700$

Therefore,

$y=3600-2700=900$

Hence $Rs.3600$ can be divided in $Rs.2700$ and $Rs.900$ respectively.