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. 1800 (b) Rs. 2000

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Solution

left parenthesis straight a right parenthesis Total space money space to space be space invested space equals space Rs. space 30000 space space Let space the space money space invested space in space the space first space bond space equals space Rs. space straight x space space therefore space money space invested space in space the space second space bond space equals space Rs. space left parenthesis 30000 space – space straight x space right parenthesis space open square brackets table row straight x 3000 cell negative straight x end cell end table close square brackets space open square brackets table row cell begin inline style 5 over 100 end style end cell row cell begin inline style 7 over 100 end style end cell end table close square brackets space equals space open square brackets table row 1800 end table close square brackets or space space space open square brackets table row cell begin inline style fraction numerator 5 straight x over denominator 100 end fraction space plus space open parentheses table row cell 3000 minus end cell straight x end table close parentheses end style end cell end table space cross times space begin inline style 7 over 100 end style close square brackets space space equals space open square brackets table row 1800 end table close square brackets therefore space begin inline style fraction numerator 5 straight x over denominator 100 end fraction end style space plus space begin inline style 7 over 100 end style space space open parentheses table row cell 3000 minus end cell straight x end table close parentheses space equals 1800 rightwards double arrow space 5 straight x plus space 210000 minus 7 straight x equals 180000 space space space space rightwards double arrow space space 2 straight x equals 30000 rightwards double arrow space space straight x equals 15000 therefore money space invested space in space two space bonds space is space Rs. space 15000 space respectively. left parenthesis b right parenthesis From space given space condition space open square brackets table row straight x 3000 cell negative straight x end cell end table close square brackets space open square brackets table row cell begin inline style 5 over 100 end style end cell row cell begin inline style 7 over 100 end style end cell end table close square brackets space equals space open square brackets table row 2000 end table close square brackets o r space space space open square brackets table row cell begin inline style fraction numerator 5 straight x over denominator 100 end fraction space plus space space open parentheses table row cell 3000 minus end cell straight x end table close parentheses 7 over 100 end style end cell end table space close square brackets space space equals space open square brackets table row 2000 end table close square brackets therefore space begin inline style fraction numerator 5 straight x over denominator 100 end fraction end style space plus space begin inline style 7 over 100 end style space space open parentheses table row cell 3000 minus end cell straight x end table close parentheses space equals table row 2000 end table rightwards double arrow space 5 straight x plus space 210000 minus 7 straight x equals table row 200000 end table space space space space rightwards double arrow space space 2 straight x equals 10000 rightwards double arrow space space straight x equals 5000 therefore money space invested space in space two space bonds space is space Rs. space 5000 comma space Rs. space 25000 space respectively.

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