Last updated at Dec. 8, 2016 by Teachoo

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Ex 3.2, 19 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: Rs 1,800 (b) Rs 2000 Let. Investment on 1st bond. = Rs x So investment on 2nd bond = Rs 30,000 โ x We represent investment per bond by matrix A Let A = [โ 8(๐ฅ@30,000โ๐ฅ)] The first bond pays 5% interest per year & The second bond pays 7% interest per year We represent interest per yer per bond by matrix B Let B = [โ 8(5%& 7%)] = [5/100 7/100] Now, Total Annual Interest = Interest per bond ร Investment per bond = BA = [5/100 7/100]_(1 ร 2) [โ 8(๐ฅ@30,000โ๐ฅ)]_(2 ร1) = [5/100 ๐ฅ" + " 7/100 " (30,000 โ" ๐ฅ") " ]_(1 ร 1) = 5/100 ๐ฅ + 7/100 (30000 โ ๐ฅ) Now in part (a) Total annual interest = Rs 1800 5/100 ๐ฅ + 7/100 (30000 โ ๐ฅ) = 1800 5๐ฅ/100 + (7 (30000 โ ๐ฅ) )/100 = 1800 (5๐ฅ + 7(30000 โ ๐ฅ ))/100 = 1800 5x + 7 (30000 โ x) = 1800 ร 100 5x + 210000 โ 7x = 180000 5x โ 7x = 180000 โ 210000 โ2x = โ 30000 x = (โ30,000)/(โ2) x = 15,000 So amount investment at 5% = x = Rs. 15,000 & amount investment at 7% = Rs (30,000 โ x) = Rs. (30,000 โ 15000 ) = Rs 15,000 Now in part (b) Total annual interest = Rs 2000 5/100 ๐ฅ + 7/100 (30000 โ ๐ฅ) = 2000 5๐ฅ/100 + (7 (30000 โ ๐ฅ) )/100 = 2000 (5๐ฅ + 7(30000 โ ๐ฅ ))/100 = 2000 5x + 7 (30000 โ x) = 2000 ร 100 5x + 210000 โ 7x = 200000 5x โ 7x = 200000 โ 210000 โ2x = โ 10000 x = (โ10,000)/(โ2) x = 5,000 So amount investment at 5% = x = Rs. 5,000 & amount investment at 7% = Rs (30,000 โ x) = Rs. (30,000 โ 5000 ) = Rs 25,000

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.