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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 – x We represent investment per bond by matrix A Let A = [■8(𝑥@30,000−𝑥)] Investment 1st bond 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 = [■8(5%& 7%)] = [5/100 7/100] Now, Total Annual Interest = Interest per bond × Investment per bond = BA = [5/100 7/100]_(1 × 2) [■8(𝑥@30,000−𝑥)]_(2 ×1) = [5/100 𝑥" + " 7/100 " (30,000 –" 𝑥") " ]_(1 × 1) = 5/100 𝑥 + 7/100 (30000 – 𝑥) Interest on 1st bond Interest on 2nd bond Now in part (a) Total annual interest = Rs 1800 5/100 𝑥 + 7/100 (30000 – 𝑥) = 1800 5𝑥/100 + (7 (30000 − 𝑥) )/100 = 1800 (5𝑥 + 7(30000 − 𝑥 ))/100 = 1800 5x + 7 (30000 – x) = 1800 × 100 5x + 210000 – 7x = 180000 5x – 7x = 180000 – 210000 –2x = – 30000 x = (−30,000)/(−2) x = 15,000 Thus, Amount investment at 5% = x = Rs. 15,000 Amount investment at 7% = Rs (30,000 – x) = Rs. (30,000 – 15000 ) = Rs 15,000 Now in part (b) Total annual interest = Rs 2000 5/100 𝑥 + 7/100 (30000 – 𝑥) = 2000 5𝑥/100 + (7 (30000 − 𝑥) )/100 = 2000 (5𝑥 + 7(30000 − 𝑥 ))/100 = 2000 5x + 7 (30000 – x) = 2000 × 100 5x + 210000 – 7x = 200000 5x – 7x = 200000 – 210000 –2x = – 10000 x = (−10,000)/(−2) x = 5,000 So, Amount investment at 5% = x = Rs. 5,000 & Amount investment at 7% = Rs (30,000 – x) = Rs. (30,000 – 5000 ) = Rs 25,000

Ex 3.2

Ex 3.2, 1

Ex 3.2, 2 (i)

Ex 3.2, 2 (ii) Important

Ex 3.2, 2 (iii)

Ex 3.2, 2 (iv)

Ex 3.2, 3 (i)

Ex 3.2, 3 (ii) Important

Ex 3.2, 3 (iii)

Ex 3.2, 3 (iv) Important

Ex 3.2, 3 (v)

Ex 3.2, 3 (vi) Important

Ex 3.2, 4

Ex 3.2, 5

Ex 3.2, 6

Ex 3.2, 7 (i)

Ex 3.2, 7 (ii) Important

Ex 3.2, 8

Ex 3.2, 9

Ex 3.2, 10

Ex 3.2, 11

Ex 3.2, 12 Important

Ex 3.2, 13 Important

Ex 3.2, 14

Ex 3.2, 15

Ex 3.2, 16 Important

Ex 3.2, 17 Important

Ex 3.2, 18

Ex 3.2, 19 Important You are here

Ex 3.2, 20 Important

Ex 3.2, 21 (MCQ) Important

Ex 3.2, 22 (MCQ) Important

Chapter 3 Class 12 Matrices (Term 1)

Serial order wise

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.