A Trust invested money in two types of bonds. The first bond pay 10% interest and second bond pays 12% interest. The trust receives 2800 as interest. However, if trust had interchanged money in bonds they would have got 100 less as interest. Use matrix method to find the amount invested by the trust.
Answers
Answer:
Rs 10,000 and Rs 15,000
Step-by-step explanation
Given A trust invests in two types of bonds. Let first type of bond be P and second type of bond be Q.
So, interest for first bond is 10% = 0.1 and second bond is 12% = 0.12
Now in matrix type we can write as
[P Q] [0.1
0.12] = 2800
0.1 p + 0.12 Q = 2800
Multiply by 10
P + 1.2 Q = 28000-----------(1)
By interchanging the bonds we get
[ Q P] = [0.1
0.12] = 2700 (since Rs 100 less)
0.1 Q + 0.12 P = 2700
Multiply by 10 we get
Q + 1.2 P = 27000------------------(2)
From 1 and 2 we get
P + 1.2 Q = 28000
1.2P + Q = 27000 multiply by 1.2
P + 1.2Q = 28000
1.44P + 1.2 Q = 32000 subtract
------------------------------------------------------
- 0.44P = - 4400
P = 10,000
P + 1.2Q = 28000
10000 + 1.2Q = 28000
1.2Q = 18000
Q = 15,000
The amount invested is Rs 10,000 and Rs 15,000
The amount invested will be Rs 10000 and Rs 15000
Let the amount invested in 10% interest = A
Let the amount invested in 12% interest = B
Hence net interest received
= 0.1A + 0.12B = 2800
=> A + 1.2B = 28000________eqn1
After interchanging the amount,
the amount invested in 10% interest = B
the amount invested in 12% interest = A
Net interest received = 2800 - 100
=> 0.12A + 0.1B = 2700
=> 1.2A + B = 27000
multiplying both side by 1.2
1.44A + 1.2B = 32400________eqn2
Subtracting eqn1 from eqn2 we get,
0.44A = 4400
=> A = 10000
putting the value of A in eqn 1 we get,
10000 + 1.2B = 28000
=> 1.2B = 18000
=> B = 18000/1.2 = 15000
Hence the amount invested will be Rs 10000 and Rs 15000