Question

An Amount of rs.4000 is distributed into
the three investment at the rate of 7%, 8% and 9%
per annum respectively.the
total anual income is Rs. 317.50 and
annum pe 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

Given :

The Amount = Rs.4,000

Distributed into three investments at the rate of 7%, 8%  and 9% per annum respectively

Total annual income is Rs. 317.50

The annual income from the first investment = Rs. 5

To find :  amount of each investment

Solution:

Investment

100 A, 100 B  and 4000 - 100 A - 100 B

4,000 - 100 A - 100 B  = 100(40 - A - B)

Interest =  100 A × 7 × 1 ÷ 100 = 7 A

= 100 B × 8 × 1 ÷ 100 = 8 B

=  100(40 - A - B) × 9 × 1 ÷ 100 = 9 ((40 - A - B) )

Now, we have

the total annual income = Rs.317.50

= 7 A + 8 B + 360 - 9 A - 9 B = 317.50

= 2 A + B = = 42.5

As we know that income from first investment is Rs. 5 that is higher than the income from the second one so the equation will be

= 7 A = 8 B + 5

2 A + B =  42.5  = 16 A + 8 B = 340

= 16 A = -8 B + 340

= 23 A = 345

= A =  15  = 100 A = 1,500

= B = 12.5 = 100 B = 1,250

4,000 - 100 A - 100 B  = 4,000 - 1,500 - 1,250  = 1,250

Therefore the amount of each investment is

= 1,500, 1,250 and 1,250

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