Question

An amount of Rs.5000 is invested in three types of investments, at interest rates 6.7, 7.7, 8%

per annum respectively. The total annual income from these investimest is Rs.350/- If the total

annual income from first two investment is Rs.70 more than the income from the third, find the

amount of each investment using matrix method.
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Answer 1

Matrix method

Correct question: An amount of Rs. 5000 is invested in three types of investments, at interest rates 6%, 7%, 8% per annum respectively. The total annual income from these investimest is Rs. 358. If the total annual income from the first two investment is Rs. 70 more than the income from the third, find the amount of each investment using matrix method.

Solution: Let the three investments done at interest rates 6%, 7% and 8% per annum respectively, be x, y and z.

• Income at 6% interest from Rs. x in a year is Rs. 6x/100.
• Income for 7% interest from Rs. y in a year is Rs. 7y/100.

• Income for 8% interest from Rs. z in a year is Rs. 8z/100.

Total income = Rs. (6x/100 + 7y/100 + 8z/100)

                      = Rs. 1/100 * (6x + 7y + 8z) .

Using the given conditions, we can formulate the following equations:

• x + y + z = 5000 .....(1)
• 6x + 7y + 8z = 35800 .....(2)
• 6x + 7y - 8z = 7000 .....(3)

*** now follow the given attachment ***

We have found the solution,

• x = 1000, y = 2200 and z = 1800.

Answer:

Hence the three investments are Rs. 1000, Rs. 2200 and Rs. 1800.