An amount of Rs. 4,000 is distributed into three investments at the rate of 7%, 8%
and 9% per annum respectively. The total annual income is Rs. 317.50 and the annual
income from the first investment is Rs. 5 more than the income from the second. Find
the amount of each investment using matrix algebra.
Answers
Answer:
Step-by-step explanation:
Firstly we consider x,y,z are the amount of investments.
Given : An amount of Rs. 4,000 is distributed into three investments at the rate of 7%, 8% and 9% per annum respectively. The total annual income is Rs. 317.50 and the annual income from the first investment is Rs. 5 more than the income from the second
To find : amount of each investment
Solution:
Investment
100A , 100B & 4000 - 100A - 100B
4000 - 100A - 100B = 100(40 - A - B)
Interest = 100A * 7 * 1 / 100 = 7A
Interest = 100B *8 * 1 / 100 = 8B
Interest = 100(40 - A - B) * 9 * 1 / 100 = 9 ((40 - A - B) )
total annual income is Rs. 317.50
= > 7A + 8B + 360 - 9A - 9B = 317.50
=> 2A + B = = 42.5
income from the first investment is Rs. 5 more than the income from the second
=> 7A = 8B + 5
2A + B = 42.5 => 16A + 8B = 340
=> 16A = -8B + 340
=> 23A = 345
=> A = 15 => 100A = 1500
=> B = 12.5 => 100B = 1250
4000 - 100A - 100B = 4000 - 1500 - 1250 = 1250
amount of each investment = 1500 , 1250 , 1250
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