the monthly incomes of Aryan and babban are in the ratio 3:4 and their monthly expenditures are in the ratio 5:7 if each saves ₹15000 per month, find their monthly incomes using matrix method. this problem reflects which value?
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Let the incomes of Aryan and Babban be 3x and 4x respectively.
Similarly, their expenditures would be 5y and 7y respectively.
Since each saves Rs. 15000, we get
3x−5y=15000...(1)
4x−7y=15000...(2)
This can be written in matrix form as [
3
4
−5
−7
][
x
y
]=[
15000
15000
]
R
2
→R
2
−
3
4
R
1
We get
⎣
⎢
⎡
3
0
−5
3
−1
⎦
⎥
⎤
[
x
y
]=[
15000
−5000
]
R
2
→R
2
×−3
We get [
3
0
−5
1
][
x
y
]=[
15000
15000
]
R
1
→R
1
+5R
2
We get [
3
0
0
1
][
x
y
]=[
90000
15000
]
R
1
→R
1
×
3
1
We get [
1
0
0
1
][
x
y
]=[
30000
15000
]
∴x=30000
Their incomes thus become Rs. 90,000 and Rs. 120,000 respectively.
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