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Question

A shopkeeper has 3 varieties of pens A,B and C. Meenu purchased 1 pen of each variety for a total of Rs. 21. Jeen purchased 4 pens of A variety, 3 pens of B variety and 2 pens of C variety for Rs. 60. While Shikha purchased 6 pens of A variety, 2 pens of B variety and 3 pens of C variety for Rs. 70. Using matrix method find the cost of each pen.

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Solution

From the given information we can form a matrix as follows :
111432623ABC=216070

Applying R2R24R1, R3R36R1

111012043ABC=212456

Applying R3R3+(4)R2

111012005ABC=212440

From above we get three equations,
A+B+C=21 ----- ( 1 )
B2C=24 ----- ( 2 )
5C=40
C=8 ------ ( 3 )
Substituting C=8 in equation ( 2 ), we get
B2(8)=24
B=24+16
B=8
Substituting value of B and C in equation ( 1 ) we get,
A+8+8=21
A+16=21
A=5
Cost of A variety pen is Rs.5, B variety pen is Rs.8 and C variety pen is Rs.8.

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