Question

A trust caring for handicapped children gets Rs.30,000 every month from its donors. The trust spends half of the funds received for medical and educational care of the children and for that it charges2% of the spent amount from them , and deposits the balance amount in privatebank to get the money multiplied so that in future the trust goes on functioning regularly. What percent of interest should the trust get from the bank to get a total of Rs.1,800 every month? Use matrix method, to find the rate of interest. Do you think people should donateto such trusts?

Answer 1

The trust gets Rs. 30000 from its donors. It spends half of the money for medical and educational purposes. Then the remaining money is Rs. 15000.
The trust charges 2% of the spent amount. 
∴, the trust earns =15000×2/100=300 in this account which can be denoted as A and the interest from the bank can be denoted by B (say). Then,
A=300 and A+B=1800
We put this in matrix form as follows:
[tex] \left[\begin{array}{cc}1&0\\1&1\end{array}\right] \left[\begin{array}{c}A&B\end{array}\right] = \left[\begin{array}{c}300&1800\end{array}\right] [/tex]

or, [tex] \left[\begin{array}{c}A&B\end{array}\right]= \left[\begin{array}{cc}1&0\\1&1\end{array}\right] ^{-1}\left[\begin{array}{c}300&1800\end{array}\right] [/tex]

or, [tex] \left[\begin{array}{c}A&B\end{array}\right]= 1/(1) \left[\begin{array}{cc}1&0\\-1&1\end{array}\right] \left[\begin{array}{c}300&1800\end{array}\right] [/tex]

or, $\left[\begin{array}{c}A&B\end{array}\right]= \left[\begin{array}{cc}1&0\\-1&1\end{array}\right] \left[\begin{array}{c}300&1800\end{array}\right]$

or, [tex] \left[\begin{array}{c}A&B\end{array}\right]= \left[\begin{array}{c}300&1500\end{array}\right] [/tex]
∴, A=300 and B=1500
If r% is the  monthly interest from the bank then,
15000×r/100=1500
or, r=1500/150
or, r=10% Ans.