Question

An amount of Rs. 4,000 is distributed into three investments at the rate of 7%, 8% and 9% per annum respectively. The total annual income is Rs. 317.50 and the annual income from the first investment is Rs. 5 more than the income from the second. Find the amount of each investment using matrix algebra.

Answer 1

Step-by-step explanation:

let x1,x2 and x3 denote the amout of first ,second and third investements

we can right,

x1+x2+x3=4000..........[1]

7x1+8x2+9x3=317.50..........[2]

0.07x1+0.08x2=5

7x1+8x2=500.....[3]

writing the above equations in matrix form

[1      1     1 ]  x1         [4000]

[7     8    9 ] x2     =  [31750]   or AX=D

[7    -8    0] x3         [500]

here A=23

A1=34500

A2=28750

A3=28750

:. x1=34500/23=RS1,500

x2=x3=28750/23=RS1,250

hope it helps