what is 3% of rs 190
Answers
Answer:
5.7
Step-by-step explanation:
3%=3/100
=190*3/100
=570/100
=5.7
Answer:
Let x,y and z be the investments at the rates of interest of 10%,12% and 15% per annum respectively.
Income from the first investment of Rs.x=Rs.
100
10x
=Rs.0.1x
Income from the second investment of Rs.x=Rs.
100
12y
=Rs.0.12y
Income from the first investment of Rs.x=Rs.
100
15z
=Rs.0.15z
∴Total annual income=Rs.(0.1x+0.12y+0.15z)
⇒0.1x+0.12y+0.15z=1310 (∵ Total annual income=Rs.1310)
It is given that the combined income from the first two incomes is Rs.190 short of the income from the third.
∴0.1x+0.12y=0.15z−190
⇒−0.1x−0.12y+0.15z=190
Thus, we obtain the following system of simultaneous linear equations:
x+y+z=10000
0.1x+0.12y+0.15z=1310
−0.1x−0.12y+0.15z=190
The given system of equation can be written in matrix form as follows:
⎣
⎢
⎢
⎡
1
0.1
−0.1
1
0.12
−0.12
1
0.15
0.15
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
10000
1310
190
⎦
⎥
⎥
⎤
AX=B
Here A=
⎣
⎢
⎢
⎡
1
0.1
−0.1
1
0.12
−0.12
1
0.15
0.15
⎦
⎥
⎥
⎤
∣A∣=1(0.15×0.12+0.15×0.12)−1(0.15×0.1+0.15×0.1)+1(−0.1×0.12+0.12×0.1)
=0.036−0.03+0=0.006
Let C
ij
be the co-factors of the elements a
ij
in A=[a
ij
].Then,
C
11
=(−1)
1+1
∣
∣
∣
∣
∣
∣
0.12
−0.12
0.15
0.15
∣
∣
∣
∣
∣
∣
=0.036
C
12
=(−1)
1+2
∣
∣
∣
∣
∣
∣
0.1
−0.1
0.15
0.15
∣
∣
∣
∣
∣
∣
=−0.03
C
13
=(−1)
1+3
∣
∣
∣
∣
∣
∣
0.1
−0.1
0.12
−0.12
∣
∣
∣
∣
∣
∣
=0
C
21
=(−1)
2+1
∣
∣
∣
∣
∣
∣
1
−0.12
1
0.15
∣
∣
∣
∣
∣
∣
=−0.27
C
22
=(−1)
2+2
∣
∣
∣
∣
∣
∣
1
−0.1
1
0.15
∣
∣
∣
∣
∣
∣
=0.25
C
23
=(−1)
2+3
∣
∣
∣
∣
∣
∣
1
−0.1
1
−0.12
∣
∣
∣
∣
∣
∣
=0.02
C
31
=(−1)
3+1
∣
∣
∣
∣
∣
∣
1
0.12
1
0.15
∣
∣
∣
∣
∣
∣
=0.03
C
32
=(−1)
3+2
∣
∣
∣
∣
∣
∣
1
0.1
1
0.15
∣
∣
∣
∣
∣
∣
=−0.05
C
33
=(−1)
3+3
∣
∣
∣
∣
∣
∣
1
0.1
1
0.12
∣
∣
∣
∣
∣
∣
=0.02
adjA=
⎣
⎢
⎢
⎡
0.036
−0.27
0.03
−0.03
0.25
−0.05
0
0.02
0.02
⎦
⎥
⎥
⎤
T
=
⎣
⎢
⎢
⎡
0.036
−0.03
0
−0.27
0.25
0.02
0.03
−0.05
0.02
⎦
⎥
⎥
⎤
X=A
−1
B
=
0.006
1
⎣
⎢
⎢
⎡
0.036
−0.03
0
−0.27
0.25
0.02
0.03
−0.05
0.02
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
10000
1310
190
⎦
⎥
⎥
⎤
=
0.006
1
⎣
⎢
⎢
⎡
360−353.7+5.7
−300+327.5−9.5
0+26.2+3.8
⎦
⎥
⎥
⎤
⇒
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
=
6
1000
⎣
⎢
⎢
⎡
12
18
30
⎦
⎥
⎥
⎤
∴x=
6
1000
×12=2000
y=
6
1000
×18=3000
z=
6
1000
×30=5000
Thus, the three investments are of Rs.2000,Rs.3000 and Rs.5000 respectively.