​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?        

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=1800300XY=1110-11800300

XY=1110-11800300XY=10-10-1-101800300XY=-10-1-111800300XY=0   11-11800300=0+3001800-300XY=3001500X=300 and Y=1500Let the monthly interest be x%, hencex% of 15000=1500x100×15000=1500x=10%

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