Question

I derive an annual income of Rs 688.25 from Rs 10000 invested partly at 8% p.a, and partly at 5% p.a. simple interest. What is the ratio of my money invested at 5% to the investment at 8%.

• A. $114:165$
• B. $51:58$
• C. $97:113$
• D. $149:251$

Answer 1

The correct option is D $149:251$

$\Rightarrow$ Let the money invested in $5\%p.a$ be $x$.

$\therefore$ Simple Interest for $5\%$ p.a = $\frac{x\times 1\times 5}{100}$ --------- ( 1 )

$\Rightarrow$ Since the investment done party,

$\therefore$ Simple Interest for $8\%$ p.a = $\frac{(10000-x)\times 1\times 8}{100}$ -------- ( 2 )

$\Rightarrow$ According to the given condition we know, $\left(1\right)+\left(2\right)=\mathrm{688.25.}$

$\Rightarrow$ $5x-8x+80000=68825$

$\Rightarrow$ $3x=11175$

$\Rightarrow$ $x=3725.$

$\therefore$ Money invested at $5\%=Rs.3725.$ and for $8\%=10000-3725=Rs.6275.$

$\Rightarrow$ Ratio of money invested at $5\%$ to the invested $8\%$ = $\frac{3725}{6275}=\frac{149}{251}$