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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.
?
Most Upvoted Answer
An amount of Rs. 4,000 is distributed into three investments at the ra...
Let x, y and z be the amounts invested at 7%, 8% and 9% respectively.
Then we have the following system of equations:
x + y + z = 4000 (total amount invested)
0.07x + 0.08y + 0.09z = 317.50 (total annual income)
0.07x = 0.08y + 5 (annual income from first investment is Rs. 5 more than second)
Rewriting the third equation, we get 0.07x - 0.08y = 5
This system of equations can be written in matrix form as:
\begin{bmatrix} 1 & 1 & 1 \\ 0.07 & 0.08 & 0.09 \\ 0.07 & -0.08 & 0 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 4000 \\ 317.50 \\ 5 \end{bmatrix}
Using a calculator or software, we can find the inverse of the coefficient matrix:
\begin{bmatrix} 1 & 1 & 1 \\ 0.07 & 0.08 & 0.09 \\ 0.07 & -0.08 & 0 \end{bmatrix}^{-1} = \begin{bmatrix} -400 & 1000 & -600 \\ 375 & -875 & 500 \\ -25 & 75 & -50 \end{bmatrix}
Multiplying both sides of the matrix equation by the inverse matrix, we get:
\begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} -400 & 1000 & -600 \\ 375 & -875 & 500 \\ -25 & 75 & -50 \end{bmatrix} \begin{bmatrix} 4000 \\ 317.50 \\ 5 \end{bmatrix} = \begin{bmatrix} 1400 \\ 1500 \\ 1100 \end{bmatrix}
Therefore, the amounts invested at 7%, 8% and 9% are Rs. 1400, Rs. 1500 and Rs. 1100 respectively.
Then we have the following system of equations:
x + y + z = 4000 (total amount invested)
0.07x + 0.08y + 0.09z = 317.50 (total annual income)
0.07x = 0.08y + 5 (annual income from first investment is Rs. 5 more than second)
Rewriting the third equation, we get 0.07x - 0.08y = 5
This system of equations can be written in matrix form as:
\begin{bmatrix} 1 & 1 & 1 \\ 0.07 & 0.08 & 0.09 \\ 0.07 & -0.08 & 0 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 4000 \\ 317.50 \\ 5 \end{bmatrix}
Using a calculator or software, we can find the inverse of the coefficient matrix:
\begin{bmatrix} 1 & 1 & 1 \\ 0.07 & 0.08 & 0.09 \\ 0.07 & -0.08 & 0 \end{bmatrix}^{-1} = \begin{bmatrix} -400 & 1000 & -600 \\ 375 & -875 & 500 \\ -25 & 75 & -50 \end{bmatrix}
Multiplying both sides of the matrix equation by the inverse matrix, we get:
\begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} -400 & 1000 & -600 \\ 375 & -875 & 500 \\ -25 & 75 & -50 \end{bmatrix} \begin{bmatrix} 4000 \\ 317.50 \\ 5 \end{bmatrix} = \begin{bmatrix} 1400 \\ 1500 \\ 1100 \end{bmatrix}
Therefore, the amounts invested at 7%, 8% and 9% are Rs. 1400, Rs. 1500 and Rs. 1100 respectively.
Community Answer
An amount of Rs. 4,000 is distributed into three investments at the ra...
2,40,000
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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. Related: Properties of Determinants - Matrices and Determinants, Business Mathematics & Statistics?
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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. Related: Properties of Determinants - Matrices and Determinants, Business Mathematics & Statistics? for B Com 2024 is part of B Com preparation. The Question and answers have been prepared according to the B Com exam syllabus. Information about 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. Related: Properties of Determinants - Matrices and Determinants, Business Mathematics & Statistics? covers all topics & solutions for B Com 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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. Related: Properties of Determinants - Matrices and Determinants, Business Mathematics & Statistics?.
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. Related: Properties of Determinants - Matrices and Determinants, Business Mathematics & Statistics? for B Com 2024 is part of B Com preparation. The Question and answers have been prepared according to the B Com exam syllabus. Information about 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. Related: Properties of Determinants - Matrices and Determinants, Business Mathematics & Statistics? covers all topics & solutions for B Com 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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. Related: Properties of Determinants - Matrices and Determinants, Business Mathematics & Statistics?.
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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. Related: Properties of Determinants - Matrices and Determinants, Business Mathematics & Statistics? in English & in Hindi are available as part of our courses for B Com.
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and 9% per annum respectively. The total annual income is Rs. 317.50 and the annual
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the amount of each investment using matrix algebra. Related: Properties of Determinants - Matrices and Determinants, Business Mathematics & Statistics? defined & explained in the simplest way possible. Besides giving the explanation of
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
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ample number of questions to practice 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. Related: Properties of Determinants - Matrices and Determinants, Business Mathematics & Statistics? tests, examples and also practice B Com tests.
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