Q. 325.0( 1 Vote )

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

Answer :

Let the varieties of pen A, B and C be x, y and z respectively.


As per the Data we get,


x + y + z = 21


4x + 3y + 2z = 60


6x + 2y + 3z = 70


These three equations can be written as



A X = B


|A| = 1(9 – 4) – 1(12 – 12) + 1(8 – 18)


= 1(5) – 1(0) + 1(– 10)


= 5 – 0 – 10


= – 5


Hence, the unique solution given by x = A – 1B


C11 = (– 1)1 + 1 (9 – 4) = 5


C12 = (– 1)1 + 2 (12 – 12) = 0


C13 = (– 1)1 + 3 (8 – 18) = – 10


C21 = (– 1)2 + 1 (3 – 2) = – 1


C22 = (– 1)2 + 2 (3 – 6) = – 3


C23 = (– 1)2 + 3 (2 – 6 ) = 4


C31 = (– 1)3 + 1 (2 – 3) = – 1


C32 = (– 1)3 + 2 (2 – 4) = 2


C33 = (– 1)3 + 3 (3 – 4) = – 1


Adj A =


X = A – 1 B =


X =


X =


=


=


Hence, A = Rs 5, B = Rs 8 and C = Rs 8

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