Question

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 \(1,800 \)
  \(B.\) Rs \(2,000\)

Answer 1

(a) Let Rs \(x\) be invested in the first bond. Then, the sum of money invested in the second bond will be Rs\( (30000 − x).\) It is given that the first bond pays \(5\)% interest per year and the second bond pays \(7%\) % interest per year. Therefore, in order to obtain an annual total interest of Rs \(1800\), we have: \(\begin{bmatrix}x&(30000-x)\end{bmatrix}\begin{bmatrix}\frac{5}{100}\\\frac{7}{100}\end{bmatrix}=1800\)  \([\)S.I for 1 year=\(\frac{Principal*Rate}{100}]\)
\(\Rightarrow\frac{5x}{100}+\frac{7(30000-x)}{100}=1800\)
\(\Rightarrow\) \(5x+210000-7x=180000\)
\(\Rightarrow\) \(210000-2x=180000\)
\(\Rightarrow\) \(2x=210000-180000\)
\(\Rightarrow\) \(x=15000\)

Thus, in order to obtain an annual total interest of Rs \(1800\), the trust fund should invest
Rs 15000 in the first bond and the remaining Rs \(15000\) in the second bond.

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(b) Let Rs \(x\) be invested in the first bond. Then, the sum of money invested in the second bond will be Rs (\(30000 − x\)).
Therefore, in order to obtain an annual total interest of Rs \(2000\), we have:
\(\begin{bmatrix}x&(30000-x)\end{bmatrix}\begin{bmatrix}\frac{5}{100}\\\frac{7}{100}\end{bmatrix}=2000\)
\(\Rightarrow \frac{5x}{100}+\frac{7(30000-x)}{100}=2000\)
\(\Rightarrow\) \(5x+210000-7x=200000\)
\(\Rightarrow\) \(2x=210000-20000\)
\(\Rightarrow\) \(x=5000\)

Thus, in order to obtain an annual total interest of Rs \( 2000,\) the trust fund should invest Rs \(5,000\) in the first bond and the remaining Rs \( 25000\) in the second bond.
 

Answer 2