Q. 443.7( 3 Votes )

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 ₹70more

than 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)

Answer :


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.


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