Question

$\huge\color{cyan}\boxed{\colorbox{black}{Question ❤}}$

A trust has Rs 30000 that must be invested in two different types of bonds. The first bond pays 5% interest per year , and second bond pays 7% interest per year. Using matrix multiplication, determine how to divide Rs 30000 among the two bonds. If the trust fund must obtain an annual total interest of
1) Rs. 1800
2) Rs. 2000

Note => Don't Spam I want correct answer ✅​

Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that

Amount invested in first type of bond be Rs x

Amount invested in second type of bond be Rs (30000 - x)

Given that, The first bond pays 5 % interest per annum and second one pays 7% interest per annum.

So, matrix form of the above data is as

$\sf \: A = \bigg[ \begin{matrix}x& 30000 - x \end{matrix} \bigg]$

$B = \left[\begin{array}{c} \dfrac{5}{100} \\ \\ \dfrac{7}{100} \end{array}\right]$

Given that,

$\sf \: Interest\:received \: = \: Rs \: 1800$

$\sf \: AB \: = \:[ 1800]$

$\sf \: \bigg[ \begin{matrix}x& 30000 - x \end{matrix} \bigg]\left[\begin{array}{c} \dfrac{5}{100} \\ \\ \dfrac{7}{100} \end{array}\right] = [ 1800]$

$\sf\: \left[x \times \dfrac{5}{100} + (30000 - x) \times \dfrac{7}{100} \right] = [ 1800]$

$\sf\: \left[ \dfrac{5x + 210000 - 7x}{100} \right] = [ 1800]$

$\sf\: \left[ \dfrac{210000 - 2x}{100} \right] = [ 1800]$

$\sf \: 210000 - 2x = 180000$

$\sf \: 2x = 210000 - 180000$

$\sf \: 2x = 30000$

$\implies\sf \: x = 15000$

Thus,

$\implies\sf \: Investment\:in\:first\:bond= Rs \: 15000$

and

$\implies\sf \: Investment\:in\:second\:bond = Rs \: 15000$

Given that,

$\sf \: Interest\:received \: = \: Rs \: 2000$

$\sf \: AB \: = \:[ 2000]$

$\sf \: \bigg[ \begin{matrix}x& 30000 - x \end{matrix} \bigg]\left[\begin{array}{c} \dfrac{5}{100} \\ \\ \dfrac{7}{100} \end{array}\right] = [ 2000]$

$\sf\: \left[x \times \dfrac{5}{100} + (30000 - x) \times \dfrac{7}{100} \right] = [ 2000]$

$\sf\: \left[ \dfrac{5x + 210000 - 7x}{100} \right] = [ 2000]$

$\sf\: \left[ \dfrac{210000 - 2x}{100} \right] = [ 2000]$

$\sf \: 210000 - 2x = 200000$

$\sf \: 2x = 210000 - 200000$

$\sf \: 2x = 10000$

$\implies\sf \: x = 5000$

Thus,

$\implies\sf \: Investment\:in\:first\:bond= Rs \: 5000$

and

$\implies\sf \: Investment\:in\:second\:bond = Rs \: 25000$

Answer 2

Answer:

25000 is the answer as it is very easy dear...

Please mark me as brainlest....