A trust gets Rs 30,000 every month from its donors The trust spends half of funds received for medical - Maths - Matrices

Question

​A trust gets Rs 30,000 every month from its donors The trust
spends half of funds received for medical and educational care of
the children and for that it charges 2% of the spent amount from
them, and deposits the balance amount in bank to get the money
multiplied so that in future the trust goes on functioning
regularly Using matrix method find the %age of interest that trust
should get from the bank to get a total of Rs 1,800 every month?
Please explain how the matrices are framed?

Shivam Mishra · Accepted Answer

Dear Student,
Please find below the solution to the asked query:

Out of ₹30000  received, the trust spends half for medical and education care
Hence the amount deposited in private bank is the remaining half=₹ 15000The trust charges 2% of the money spent for medical and educational care
Hence the earning of trust from above charges is 2% of 15000=2100×15000=₹3000Let the earning of trust from above charges be X and the earning from interestobtained from bank be Y
 Hence we get:X+Y=1800 ;iX=300 orX+0Y=300 ;ii1110XY=1800300Here 1110 represents coefficient of X and Y in equation i and ii along the rwoElements in first row are 1 and 1 because coefficients of X and Y in iare 1 and 1 repsectivelyElements in second row are 1 and 0 because coefficients of X and Y in iare 1 and 0 repsectively
Again1110XY=1800300⇒XY=1110-11800300
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_56e68a18d77b3%20png"
style="width: 284px; height: 102px;">
⇒XY=1110-11800300⇒XY=10-10-1-101800300⇒XY=-10-1-111800300⇒XY=0   11-11800300=0+3001800-300⇒XY=3001500⇒X=₹300 and Y=₹1500Let the monthly interest be x%, hencex% of 15000=1500⇒x100×15000=1500⇒x=10%

Hope this information will clear your doubts about this topic

If you have any doubts just ask here on the ask and answer forum
and our experts will try to help you out as soon as possible
Regards