Question

You have \[Rs.12,000\] saved and want to invest it in two schemes yielding \[10\% \] and \[15\% \] interest. How about each scheme so that you should get overall \[12\% \] interest.

Answer 1

Hint: In the given question, we had some specific saved amount and we want to invest it in two schemes yielding \[10\% \] and \[15\% \] interest. We have to find out how each scheme will be arranged so that we will get overall \[12\% \] interest. In this we have to find out the amount on which interest of \[10\% \] and \[15\% \] is applied and the total amount will equal to the \[12\% \] of the interest.

Complete step-by-step answer:
In the question, we had given \[Rs{\text{ }}12000\] as a saved amount and we wanted to invest it in two schemes yielding \[10\% \] and \[15\% \]interest. Then further we had asked how each scheme is there so that we will get \[12\% \] interest overall.
First of all we are given a total amount \[Rs{\text{ }}12000\]and we have to deposit it in the bank under two schemes, one is having \[10\% \] interest and another is having \[15\% \] interest.
Here we will assume that the amount that has to be saved at \[10\% \] interest will be \[Rs{\text{ }}x\] and the amount that has to be saved at \[155\] interest will be \[Rs{\text{ }}y\]
That means \[10\% \] of \[x\] and \[15\% \]of \[y\] is equal to \[12\% \] of \[12000\]. This was the given condition that how much amount is there for which \[10\% \] of that and \[15\% \] of other will be equal to \[12\% \] of the \[12000\], it means we have to find out \[x\] and \[y\].
Therefore \[10\% {\text{ }}\]of \[x\]\[ + 15\% \] of \[y\] \[ = 12\% {\text{ }}12000\]
Here we will calculate percent
\[\dfrac{{10}}{{100}}x + \dfrac{{15}}{{100}}y = \dfrac{{12}}{{100}} \times 12000\]
We get \[10x + 15y = 144000........(1)\]
Also, we are given that \[x\] and \[y\] are the fractions of the total amount \[Rs{\text{ }}12000\]
That means \[x + y = 12000.......(2)\]
From \[2\]we will find the value of \[x\]
\[x{\text{ }} = {\text{ }}12000 - y.......(3)\]
Put this value of \[x\] in \[1\] , we get
\[10\left( {12000 - y} \right){\text{ }} + {\text{ }}15y{\text{ }} = {\text{ }}144000\]
\[ \Rightarrow 12000 - 10y{\text{ }} + {\text{ }}15y{\text{ }} = {\text{ }}144000\]
Which on solving for y and constant term, we get
\[5y = 144000 - 120000\]
\[ \Rightarrow 5y = 24000\]
Taking \[5\] on right hand side we get
\[y = \dfrac{{24000}}{5}\]
We get \[y{\text{ }} = {\text{ }}4800\]
Put value of \[y\] in \[3\], we get
\[X{\text{ }} = {\text{ }}12000{\text{ }} - {\text{ }}4800\]
\[ \Rightarrow {\text{x }} = {\text{ }}72000\]
Which means \[Rs{\text{ }}72000\] is deposited at the rate of \[10\% \] and \[Rs{\text{ }}48000\] is deposited at the rate of \[15\% \] which is equal to \[12\% \] of total amount that is \[12000\].

Note: Rate of interest that is applied on some specific or certain amount is always in percentage. That means at what percent the amount is having rate of interest and this rate of interest for any amount can be calculated by multiplying the rate upon \[100\] to the given amount \[100\] is divided to \[R\] because rate of interest is in percent and we will find the amount that is equal to given percent rate of interest.