Question

Two investments totaling $56,000 produce an annual income of $1400. One investment yields 4% per year, while the other yields 2% per year. How much is invested at each rate?

Answer 1

$\huge \bf \mathfrak{answer}$

42,000 and 14,000

STEP-BY-STEP VERIFICATION:

Let, one investment be x and another be 56,000-x.

Then,

Income from first investment

\begin{lgathered}= 2\% \: of \: x \\ = 0.02x\end{lgathered}

=2%ofx

=0.02x

Again,

Income from second investment

\begin{lgathered}= 4\% \: of \: (56000 - x) \\ = 2240 - 0.04x\end{lgathered}

=4%of(56000−x)

=2240−0.04x

So,

Total income=I¹+I²

Or,

\begin{lgathered}1400 = 2240 - 0.04x + 0.02x \\\end{lgathered}

1400=2240−0.04x+0.02x

Or,

840 = 0.02x840=0.02x

•°•

x = 42000x=42000

Again,

Another investment

\begin{lgathered}= 56000-42000 \\ = 14000\end{lgathered}

=56000−42000

=14000

So, the two investments are Rs. 42,000 and Rs. 14,000.