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Question
An amount of ₹ 65,000 is invested in three bonds at the rates of 6%, 8% and 9% per annum respectively. The total annual income is ₹ 4,800. The income from the third bond is ₹ 600 more than that from the second bond. Determine the price of each bond. (Use Gaussian elimination method.)
Solution
Let the amounts of 3 bounds be x, y, z
x + y + z = 65,000
`(6x)/00 + (8y)/100 + (9z)/100` = 4800
6x + 8y + 9z = 480000
`(9z)/100 = 600 + (8y)/100`
9z = 60000 + 8y
0x – 8y + 9z = 60000
Augmented martix
[A | B] = `[(1, 1, 1, |, 65000),(6, 8, 9, |, 480000),(0, -8, 9, |, 60000)]`
`{:("R"_2 -> "R"_2 - 6"R"_1),(->):} [(1, 1, 1, |, 65000),(0, 2, 3, |, 90000),(0, -8, 9, |, 60000)]`
`{:("R"_3 -> "R"_3 + 4"R"_2),(->):} [(1, 1, 1, |, 65000),(0, 2, 3, |, 90000),(0, 0, 21, |, 402000)]`
Writing the equivalent equations from echelon from.
x + y + z = 65000 ........(1)
2y + 3z = 90000 ........(2)
21z = 42000
z = 20000
(2) ⇒ 2y = 90000 – 3 × 20000
2y = 30000
y = 15000
(1) ⇒ x + 15000 + 20000 = 65000
x = 30000
∴ x = 30000, y = 15000, z = 20000
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