Question

An amount of 4000 is distributed into three investment at the rate of 7%,8%&9% per annum respectively.the total annual income 317.50 and the annual income from the first investment is rs 5 more than the income from second. Final the amount of each investment using matrix algebra

Answer 1

Given: An amount of 4000 is distributed into three investment at the rate of 7%, 8% and 9% per annum respectively.

To find: The amount of each investment using matrix algebra?

Solution:

• Let the investment be:

                  100x  , 100y  & 4000 - 100x - 100y

• So:

                  4000 - 100x - 100x  = 100(40 - x - y)

• Now we have given the interest 7%, 8% and 9%, we have:

                  =  100x ( 7(1) / 100 ) = 7x

                  =  100y ( 8(1) / 100 ) = 8y

                  =  100(40 - x - y) (9(1) / 100 )

                  =  9 ((40 - x - y))

• Now we have given that the total annual income is Rs. 317.50

• So:

                  7x + 8y + 360 - 9x - 9y = 317.50

                  2x + y = 42.5

• According to the question, income from the first investment is Rs. 5 more than the income from the second, so we have:

                  7x = 8y + 5 ..............(i)

                  2x + y =  42.5

• Multiplying by 8 on both sides, we get:  

                  16x + 8y = 340

                  16x = -8y + 340

• Putting (i) in above equation, we get:

                  16x = -(7x-5) + 340

                  23x = 345

                  x =  15  

                  100x = 1500

• Putting x = 15 in i, we get:

                  105 = 8y + 5

                  8y = 100

                  y = 12.5

                  100y = 1250

• So the amount is:

                  4000 - 100x - 100y  = 4000 - 1500 - 1250  =  1250

Answer:

              So the amount of each investment is 1500 , 1250 , 1250.