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Ex 3.2, 19 - A trust fund has Rs 30,000 that must be invested - Statement questions - Multiplication of matrices

  1. Chapter 3 Class 12 Matrices
  2. Serial order wise
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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(๐‘ฅ@30,000โˆ’๐‘ฅ)] 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(๐‘ฅ@30,000โˆ’๐‘ฅ)]_(2 ร—1) = [5/100 ๐‘ฅ" + " 7/100 " (30,000 โ€“" ๐‘ฅ") " ]_(1 ร— 1) = 5/100 ๐‘ฅ + 7/100 (30000 โ€“ ๐‘ฅ) Now in part (a) Total annual interest = Rs 1800 5/100 ๐‘ฅ + 7/100 (30000 โ€“ ๐‘ฅ) = 1800 5๐‘ฅ/100 + (7 (30000 โˆ’ ๐‘ฅ) )/100 = 1800 (5๐‘ฅ + 7(30000 โˆ’ ๐‘ฅ ))/100 = 1800 5x + 7 (30000 โ€“ x) = 1800 ร— 100 5x + 210000 โ€“ 7x = 180000 5x โ€“ 7x = 180000 โ€“ 210000 โ€“2x = โ€“ 30000 x = (โˆ’30,000)/(โˆ’2) 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 ๐‘ฅ + 7/100 (30000 โ€“ ๐‘ฅ) = 2000 5๐‘ฅ/100 + (7 (30000 โˆ’ ๐‘ฅ) )/100 = 2000 (5๐‘ฅ + 7(30000 โˆ’ ๐‘ฅ ))/100 = 2000 5x + 7 (30000 โ€“ x) = 2000 ร— 100 5x + 210000 โ€“ 7x = 200000 5x โ€“ 7x = 200000 โ€“ 210000 โ€“2x = โ€“ 10000 x = (โˆ’10,000)/(โˆ’2) 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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