a person invested 10000 rupees in three types of Bond one can carry 5% second and third type of Bond carry 6% in 7% of interest at the end of the year he got rupees 600 interest is the interchange fees amount of 5% and 6% born then he would have to get rupees 650 as interest find the amount of each type of Bond
Answers
Step-by-step explanation:
ANSWER
It is given that Rs.30,000 must be invested into two types of bonds with 5% and 7% interest rates.
Let Rs.x be invested in bonds of the first type.
Thus, Rs.(30000−x) will be invested in the other type.
Hence, the amount invested in each type of the bonds can be represented in matrix form with each column corresponding to a different type of bond as :
X=[
x
30000−x
]
A) Annual interest obtained is Rs.1800.
We know, Interest=
100
PTR
Here, the time is one year and thus T=1
Hence, the interest obtained after one year can be expressed in matrix representation as -
[
x
30000−x
]
⎣
⎢
⎢
⎡
100
5
100
7
⎦
⎥
⎥
⎤
=[1800]
⇒ [x×
100
5
+(30000−x)×
100
7
]=[1800]
⇒
100
5x
+
100
7(30000−x)
=1800
⇒ 5x+210000−7x=180000
⇒ −2x=−30000
∴ x=15000
Amount invested in the first bond =x=Rs.15000
⇒ Amount invested second bond =Rx(30000−x)=Rs.(30000−15000)=Rs.15000
∴ The trust has to invest Rs.15000 each in both the bonds in order to obtain an annual interest of Rs.1800
B) Annual interest obtained is Rs.2000.
Hence, the interest obtained after one year can be expressed in matrix representation as -
[
x
30000−x
]
⎣
⎢
⎢
⎡
100
5
100
7
⎦
⎥
⎥
⎤
=[2000]
⇒ [x×
100
5
+(30000−x)×
100
7
]=[2000]
⇒
100
5x
+
100
7(30000−x)
=2000
⇒ 5x+210000−7x=200000
⇒ −2x=−10000
∴ x=5000
Amount invested in the first bond =x=Rs.5000
⇒ Amount invested second bond =Rx(30000−x)=Rs.(30000−5000)=Rs.25000
∴ The trust has to invest Rs.5000 in the first bond and Rs.25000 in the second bond in order to obtain an annual interest of Rs.2000