A trust caring for handicapped children gets Rs 30000 every month from its donors. The trust spends half of the funds received for medical & educational care of the children & for that it charges 2% of the spent amount from them, & deposited the balance amount in a private bank to get the money multiplied so that the trust goes on functioning regularly. What percent of interest should the trust get from the bank so as to get a total of Rs. 1800 every month? Use the matrix method to find the rate of interest.

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20%

30%

10%

40%

answer is C.

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Detailed Solution

As we have a system of linear equations in two variables:

So, by using matrix method, we can write:

Now, by separating the variables on one side, we can write:
Question Image

So, we can write equation (4) as:

Now, solve the matrix, to get the value of y:
Question Image

Therefore,

Now, by using the formula:

, we get the interest rate r as:

Hence, the interest rate is 10%
So, option 3 is correct.

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