Math, asked by sbp981, 10 hours ago

4. गौतमने 80 लाल चेंडू ₹ 3 प्रतिदराने व 60 पिवळे चेंडू ₹ 4 प्रतिदराने खरेदी केले व सर्व चेंडू
40
समान दराने विकले तेव्हा त्याला एकूण 75% नफा झाला; तर त्याला प्रत्येक पिवळ्या चेंडूमागे
16किती रुपये नफा झाला?​

Answers

Answered by gyaneshwarsingh882
0

Answer:

Step-by-step explanation:

Let the cost of 1 kg onion , 1 kg wheat and 1 kg of rice be Rsx,Rsy,Rsz respectively.

So, 4x+3y+2z=60

2x+4y+6z=90

6x+2y+3z=70

These equations can be written as

AX=B

where A=  

 

4

2

6

 

3

4

2

 

2

6

3

 

,X=  

 

x

y

z

 

,B=  

 

60

90

70

 

 

Here,  

∣A∣=4(12−12)−3(6−36)+2(4−24)

⇒∣A∣=90−40=50

Since, ∣A∣

=0

Hence, the system of equations is consistent and has a unique solution given by X==A  

−1

B

A  

−1

=  

∣A∣

adjA

 and adjA=C  

T

 

C  

11

=(−1)  

1+1

 

 

4

2

 

6

3

 

 

⇒C  

11

=12−12=0

C  

12

=(−1)  

1+2

 

 

2

6

 

6

3

 

 

⇒C  

12

=−(6−36)=30

C  

13

=(−1)  

1+3

 

 

2

6

 

4

2

 

 

⇒C  

13

=4−24=−20

C  

21

=(−1)  

2+1

 

 

3

2

 

2

3

 

 

⇒C  

21

=−(9−4)=−5

C  

22

=(−1)  

2+2

 

 

4

6

 

2

3

 

 

⇒C  

22

=12−12=0

C  

23

=(−1)  

2+3

 

 

4

6

 

3

2

 

 

⇒C  

23

=−(8−18)=10

C  

31

=(−1)  

3+1

 

 

3

4

 

2

6

 

 

⇒C  

31

=18−8=10

C  

32

=(−1)  

3+2

 

 

4

2

 

2

6

 

 

⇒C  

32

=−(24−4)=−20

C  

33

=(−1)  

3+3

 

 

4

2

 

3

4

 

 

⇒C  

33

=16−6=10

Hence, the co-factor matrix is C=  

 

0

−5

10

 

30

0

−20

 

−20

10

10

 

 

⇒adjA=C  

T

=  

 

0

30

−20

 

−5

0

10

 

10

−20

10

 

 

⇒A  

−1

=  

∣A∣

adjA

=  

50

1

 

 

0

30

−20

 

−5

0

10

 

10

−20

10

 

 

Solution is given by  

 

x

y

z

 

=  

50

1

 

 

0

30

−20

 

−5

0

10

 

10

−20

10

 

 

 

60

90

70

 

 

 

x

y

z

 

=  

50

1

 

 

0−450+700

1800+0−1400

−1200+900+700

 

 

 

x

y

z

 

=  

50

1

 

 

250

400

400

 

 

 

x

y

z

 

=  

 

5

8

8

 

 

Hence, x=5,y=8,z=8

So, the cost of 1 kg onion is Rs 5 , 1 kg wheat  is Rs 8 , 1 kg rice is Rs 8.

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