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)

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

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Determinants of Matrices of different order59 mins  Determining a determinant63 mins  Types of Matrices & Properties51 mins  Interactive Quiz on Matrices and Determinants41 mins  Triangular Matrices & operations on matrices58 mins  Know About finding the Adjoint & Inverse Of Matrix46 mins  Interactive Quiz on Properties of Determinants43 mins  Lecture on Product of Determinants58 mins  Test Yourself, Properties of Determinants30 mins  Interactive Quiz on Matrices & Determinants48 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 