Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XII  >>  Math  >>  Matrices
0 votes

A trust fund has Rs 30,000 that must be invested in two different types of bonds. The first bond pays 5% interest per year, and the second bond pays 7% interest per year. Using matrix multiplication, determine how to divide Rs 30,000 among the two types of bonds. If the trust fund must obtain an annual total interest of: a) Rs. 1800.

  This question has 2 parts and each part has been answered separately here.
Can you answer this question?

1 Answer

0 votes
  • Multiplication of two matrices is defined only if the number of columns of the left matrix is the same as the number of rows of the right matrix.
  • If A is an m-by-n matrix and B is an n-by-p matrix, then their matrix product AB is the m-by-p matrix whose entries are given by dot product of the corresponding row of A and the corresponding column of B: $\begin{bmatrix}AB\end{bmatrix}_{i,j} = A_{i,1}B_{1,j} + A_{i,2}B_{2,j} + A_{i,3}B_{3,j} ... A_{i,n}B_{n,j}$
  • With these type of word problems, we need to set up the correct matrix multiplication and solve for the unknown variables.
Let $Rs.30,000$ be divided into two parts. Assume that the amount invested in the first bond as $x$, then the amount invested in the second one is $Rs(30,000-x)$.
We are given that the first bond pays $5\%$, i,e., $0.05$ in interest and the second bond $7\%$, i.e., $0.07$.
We can represent the problem using matrix multiplication as the following $1\times 2$ matrix: $\begin{bmatrix}x & 30000-x\end{bmatrix}\begin{bmatrix}0.05\\0.07\end{bmatrix}$ which is equal to the interest earned $Rs. 1800$.
Given $\begin{bmatrix}x & 30000-x\end{bmatrix}\begin{bmatrix}0.05\\0.07\end{bmatrix} = 1800$:
$\begin{bmatrix}x\times (0.05)+(30000-x)\times 0.07\end{bmatrix} = 1800$
$0.05x + 2100 - 0.07x = 1800$
$2100 - 0.02x = 1800$
$2100-1800 = 0.02x$
$0.02x = 300 \rightarrow x = \frac{1}{0.02}300$
Solving for $x$, $x = 15,000$ and $30,000-x = 15,000$.
Hence the amount has to be divided equally into two sums of $Rs.15,000$ each.
answered Mar 1, 2013 by balaji.thirumalai

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App