HSC Science (Computer Science) 12th Board ExamMaharashtra State Board
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# Solution - The cost of 4 dozen pencils, 3 dozen pens and 2 dozen erasers is Rs. 60. The cost of 2 dozen pencils, 4 dozen pens and 6 dozen erasers is Rs. 90 whereas the cost of 6 dozen pencils, 2 dozen pens and 3 dozen erasers is Rs. 70. Find the cost of each item per dozen by using matrices. - HSC Science (Computer Science) 12th Board Exam - Mathematics and Statistics

ConceptElementary Operation (Transformation) of a Matrix

#### Question

The cost of 4 dozen pencils, 3 dozen pens and 2 dozen erasers is Rs. 60. The cost of 2 dozen pencils, 4 dozen pens and 6 dozen erasers is Rs. 90 whereas the cost of 6 dozen pencils, 2 dozen pens and 3 dozen erasers is Rs. 70. Find the cost of each item per dozen by using matrices.

#### Solution

Let Rs.’x’, Rs.’y’ and Rs.’z’ be the cost of one dozen pencils, one dozen pens and one dozen erasers.
Thus, the system of equations are:

{:(4x+3y+2z=60),(2x+4y+6z=90),(6x+2y+3z=70):}

Let us write the above equations in the matrix form as:

[[4,3,2],[2,4,6],[6,2,3]][[x],[y],[z]]=[[60],[90],[70]] " i.e "AX=B

"Using "R_z->R_2-1/2R_1 and R_3->R_3-3/2R_1

[[4,3,2],[0,5/2,5],[0,-5/2,0]][[x],[y],[z]]=[[60],[60],[-20]]

"Using "R_3->R_3+R_2

[[4,3,2],[0,5/2,5],[0,0,0]][[x],[y],[z]]=[[60],[60],[40]

As matrix A is reduced to its upper triangular form we can write

4x + 3y + 2z = 60..........(i)

5/2y + 5z = 60..........(ii)

5z = 40
z = 8.....(iii)

Substituting (iii) in (ii) we get,

5/2y + 5(8) = 60

y = 8.....(iv)

Substituting (iii) and (iv) in (i) we get,
4x + 3 (8) + 2 (8) = 60
x = 5

∴ Cost of one dozen pencils, one dozen pens and one dozen erasers is Rs. 5, Rs. 8 and Rs. 8 respectively

Is there an error in this question or solution?

#### APPEARS IN

2015-2016 (March) (with solutions)
Question 2.2.3 | 4 marks
2015-2016 (July) (with solutions)
Question 3.2.2 | 4 marks

#### Reference Material

Solution for question: The cost of 4 dozen pencils, 3 dozen pens and 2 dozen erasers is Rs. 60. The cost of 2 dozen pencils, 4 dozen pens and 6 dozen erasers is Rs. 90 whereas the cost of 6 dozen pencils, 2 dozen pens and 3 dozen erasers is Rs. 70. Find the cost of each item per dozen by using matrices. concept: null - Elementary Operation (Transformation) of a Matrix. For the courses HSC Science (Computer Science), HSC Science (General) , HSC Arts, HSC Science (Electronics)
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