# An amount of ₹ 5000 is put into three investments at 6%, 7% and 8% per annum respectively. The total annual income from these investments is ₹358. If the total annual income from first two investments is ₹70morethan the income from the third, find the amount of each investment by the matrix method.HINT: Let these investments be ₹x, ₹y and ₹z, respectively.Then, x + y + z = 5000, …(i) = 358 6x + 7y + 8z = 35800 …(ii)And, 6x + 7y - 8z = 7000. …(iii)

Let these investments be ₹x, ₹y and ₹z, respectively.

Then, x + y + z = 5000

= 358

6x + 7y + 8z = 35800

And,

6x + 7y - 8z = 7000.

Representing in the matrix form,

AX = B

R3 – R2

R2 – 6R1

Converting back into the equations we get

X + y + z = 5000

Y + 2z = 5800

- 16z = - 28800

Z = 1800

Y + 2×1800 = 5800

Y = 5800 - 3600

Y = 2200
x + 2200 + 1800 = 5000

X = 5000 – 4000

X = 1000

Amount of 1000 , 2200 , 1800 were invested in the investments of 6% , 7%, 8% respectively.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Functional Equations - JEE with ease48 mins
Immune System Disorders60 mins
Female reproductive system58 mins
Female reproductive system46 mins
Rotational Kinetic Energy43 mins
Interactive Quiz | Questions based on torque & angular momentum44 mins
Interactive Quiz: Important Questions Based on Moment of Inertia35 mins
Pure Rolling49 mins
Female Reproductive System | Interactive Quiz39 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