Question

Bhagwanti inherited Rs. 12000.00, she invested part of it as 10% and the rest at 12%. Her annual income from these investments is Rs. 1280.00. How much did she invest each rate?

Answer 1

Hint: Assume that she invested Rs. ‘$x$’ as 10% and therefore, Rs. $(12000-x)$ at the rate of 12%. Calculate the sum of 10% of $x$ and 12% of $(12000-x)$ and substitute this value equal to 1280 and calculate the value of $x$.

Complete step-by-step solution -

This question can be solved by using the concept of linear equations. In mathematics, linear equation is an equation that may be put in the form $ax+by+c=0$, where $a,b\text{ and }c$ are constants and $x\text{ and }y$ are variables. When we plot a graph of a linear equation, it forms a straight line.
Now, we come to the question, total money Bhagwanti inherited = Rs. 12000.
Let us assume that she invested Rs. ‘$x$’ as 10% and therefore the remaining part, that is Rs. $(12000-x)$ at the rate of 12%.
Therefore, 10% of $x$=$\dfrac{10}{100}\times x=\dfrac{x}{10}\text{ }......................................\text{(i)}$
 And, 12% of $(12000-x)$=$\dfrac{12}{100}\times \left( 12000-x \right)\text{ }.......................\text{(ii)}$
Now, according to question,
 $10\%\text{ of }x+12\%\text{ of (12000}-x)=1280$
 $\therefore \dfrac{x}{10}+\dfrac{12\times (12000-x)}{100}=1280$
 $\dfrac{10x+12\times 12000-12x}{100}=1280$
 $\dfrac{144000-2x}{100}=1280$
 $144000-2x=128000$
 $2x=144000-128000$
 $2x=16000$
 $x=8000$
$\therefore 12000-x=12000-8000=4000$
Hence, she invested Rs. 8000 at 10% rate and Rs. 4000 at 12% rate.

Note: We have solved it as a linear equation in one variable. We can also solve it as a linear equation in two variables by considering that she invested Rs. $x$ at 10% rate and Rs. $y$ at 12% rate. Now, the sum of these must be equal to 1280 and the sum of $x$ and $y$ must be equal to 12000. These will form a system of linear equations having two variables. Solving these will give the same result.