Question

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.
(b) A wholesaler of pencils charges Rs. 24 per dozen on orders of 50 dozens or less. For
orders in excess of 50 dozens, the price is reduced by 20 paise per dozen in excess of
50 dozens. Find the size of the order that maximizes his total revenue.
(c) A computer is purchased for Rs. 50,000. It is estimated to depreciate at 10% per
annum every year. Find its scrap value at the end of 12 years.

Answer 1

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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