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Ncert Solutions Maths class 12th Maths Class 12th Matrices

29. A trust fund has ? 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 ? 30,000 among the two types of bonds. If the trust fund must obtain an annual total interest of:

(a) 1800 (b) 2000

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Answered by

Vishal Baghel | Contributor-Level 10

5 months ago

let x be the investment in the first bond out of total '30,000.

(M) then, investment use for the second bond = ' 30,000 - x.

Hence, investment matrix A = ${[x 30, 000 - x]}_{1 \times 2}$

As there is 5% and 7% interest paid the first and second , (per year)

$\begin{array}{l} = {[x \times \frac{5}{100} + (30000 - x) \times \frac{7}{100}]}_{1 \times 1} \\ = \frac{5 x + 2, 10, 000 - 7 x}{100} = \frac{2, 10, 000 - 2 x}{100 .} \end{array}$

Manual total interest = ' $\frac{210, 000 - 2 x}{100 .}$

(a) Given, manual total interest = ' 1800.

$\Rightarrow' \frac{2, 10, 000 - 2 x}{100} =' 1800 .$

$\Rightarrow' 2, 10, 000 - 2 x =' 1.80, 000$

' 210.000 - '180,000 = 2x

$\Rightarrow x =' \frac{30, 000}{2}$

x = ' 15, 000

∴investment in first and second bond is x = 15,000 and ' 30,000 –x = ' 30,000 - '15,000 - ' 15,000 respectively.

(b) Given ,Annual total interest = ' 2000.

$\Rightarrow \frac{' 2, 10, 000 - 2 x}{100} =' 2000 .$

' 2,10, 000 - ' 2,00,000

' 2,10, 000 - '2; 000 = 2x

$\Rightarrow x =' \frac{10, 500}{2}$

x = ' 5,000

∴investment in first and second hand is x = $'$ &nbs

...more

let x be the investment in the first bond out of total '30,000.

(M) then, investment use for the second bond = ' 30,000 - x.

Hence, investment matrix A = ${[x 30, 000 - x]}_{1 \times 2}$

As there is 5% and 7% interest paid the first and second , (per year)

$\begin{array}{l} = {[x \times \frac{5}{100} + (30000 - x) \times \frac{7}{100}]}_{1 \times 1} \\ = \frac{5 x + 2, 10, 000 - 7 x}{100} = \frac{2, 10, 000 - 2 x}{100 .} \end{array}$

Manual total interest = ' $\frac{210, 000 - 2 x}{100 .}$

(a) Given, manual total interest = ' 1800.

$\Rightarrow' \frac{2, 10, 000 - 2 x}{100} =' 1800 .$

$\Rightarrow' 2, 10, 000 - 2 x =' 1.80, 000$

' 210.000 - '180,000 = 2x

$\Rightarrow x =' \frac{30, 000}{2}$

x = ' 15, 000

∴investment in first and second bond is x = 15,000 and ' 30,000 –x = ' 30,000 - '15,000 - ' 15,000 respectively.

(b) Given ,Annual total interest = ' 2000.

$\Rightarrow \frac{' 2, 10, 000 - 2 x}{100} =' 2000 .$

' 2,10, 000 - ' 2,00,000

' 2,10, 000 - '2; 000 = 2x

$\Rightarrow x =' \frac{10, 500}{2}$

x = ' 5,000

∴investment in first and second hand is x = $'$ 5,000 and. $'$ 30,000 - x = 30,000 - $'$ 5,000 = 25,000 respectively

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