Q. 375.0( 1 Vote )

A total amount of ₹7000 is deposited in three different saving bank accounts with annual interest rates of 5%, 8% and respectively. The total annual interest from these three accounts is ₹550. Equal amounts have been deposited in the 5% and 8% savings accounts. Find the amount deposited in each of the three accounts, with the help of matrices.(CBSE 2014)

Answer :

Let the deposited be x, y and z respectively.


As per the Data we get,


x + y + z = 7000


5%x + 8%y + 8.5%z = 550


i.e 5x + 8y + 8.5z = 55000


x – y = 0


These three equations can be written as



A X = B


|A| = 1(0 + 8.5) – 1(0 – 8.5) + 1(– 5 – 8)


= 1(8.5) – 1(– 8.5) + 1(– 13)


= 8.5 + 8.5 – 13


= 4


Hence, the unique solution given by x = A – 1B


C11 = (– 1)1 + 1 (0 + 8.5) = 8.5


C12 = (– 1)1 + 2 (0 – 8.5) = 8.5


C13 = (– 1)1 + 3 (– 5 – 8) = – 13


C21 = (– 1)2 + 1 (0 + 1) = – 1


C22 = (– 1)2 + 2 (0 – 1) = – 1


C23 = (– 1)2 + 3 (– 1 – 1 ) = 2


C31 = (– 1)3 + 1 (8.5 – 8) = 0.5


C32 = (– 1)3 + 2 (8.5 – 5) = – 3.5


C33 = (– 1)3 + 3 (8 – 5) = 3


Adj A =


X = A – 1 B =


X =


X =


X =


=


Hence, x = 1125, y = 1125 and z = 4750

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