question_answer 29)

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 truest fund must obtain an annual total interest of : (a) Rs.1800 (b) Rs.2000  

Answer:

Let Money invested in the first type of bond =Rs.x       Money invested in the second type of bond       =Rs. (30000 ? x)        row matrix A = |x 30000 ? x| represens       Investment and a column matrix       = [1800]              5x + 210000 ? 7x = 180000        2x = 30000  x = 15000.       Investment in first type of bond is Rs.15000 and that in the second type of bond is Rs.(30,000 ? 15,000) = Rs.15,000.       (b) Total annual interest is given by product       AB = [x 30,000 ? x]       = [2000]              5x + 2,10,000 ? 7x = 2,00,000        2x = 10,000  x = 5000.        Investmentin first type of bond is Rs.5000 and that in the second type of bond is Rs.(30,000 ? 5,000) = Rs.25,000).