Mr X has invested A part of his investment in Bond A carrying interest of 10%and C part in Bond B with interest of 15%.his interest income during first year is rs. 4000.if the invest 20%more in 10%Bond A and 10% more in 15% bond B, his income during second year increase by rs. 500. find his initial investment and the new investment in Bond A and B using matrix method.
Answers
Answer:
Step-by-step explanation:
Let Rs. x and Rs. y be the initial investment in 10% bond A and 15% bond B, respectively.
Then, according to the given condition, we have
(0.10)x+(0.15)y=4000
and (0.10)(x+20100x)+(0.15)(y+10100y)=4500 ⇒
2x+3y=80000 (i) [Multiplying both sides by 20]
and (0.10)(120x)+(0.15)(110y)=450000
and 8x+11y=300000 (ii) [divide both sides by 1.5] Now, these equations can be written in matrix form as
AX = B
(iii) Where,
A=[28311],
X=[xy] and
B=[80000300000]
Here, |A|=[28311]=22−24=−2≠0
∴ A−1 exists. Now, A−1=1|A|[11−8−32]
∵ ifA=[acbd] then A−1=1|A|[d−c−ba]]
=−12[11−8−32]
Now from Eq. (iii) we have
X=A−1B=−12[11−8−32][80000300000] =−12[880000−900000−640000+600000]
=−12[−20000−40000]=[1000020000] ⇒
[xy]=[1000020000] ⇒ x=10000
and y=20000|
Hence, Mr. X invested Rs. 10000 in bond A and Rs. 20000 in bond B.