Q. 315.0( 5 Votes )

A salesman has th

Answer :

Given: - Record of sales during three months


Let, rates of commissions on items A,B and C be x, y and z respectively.


Now, we can arrange this model in linear equation system


Thus, we have


90x + 100y + 20z = 800


130x + 50y + 40z = 900


60x + 100y + 30z = 850


Here



Applying,



Solving determinant, expanding along 2nd column


D = 50[( – 50)( – 170) – ( – 200)( – 60)]


D = 50[8500 – 12000]


D = – 175000


Again, Solve D1 formed by replacing 1st column by B matrices


Here




Applying,



Solving determinant, expanding along 2nd column


D1 = 50[( – 1000)( – 500) – ( – 950)( – 60)]


D1 = 50[50000 – 57000]


D1 = – 350000


Again, Solve D2 formed by replacing 2nd column by B matrices


Here




Applying,



Solving determinant, expanding along 1st Row


D2 = 20[17500 – 52500]


D2 = – 700000


And, Solve D3 formed by replacing 3rd column by B matrices


Here




Applying,



Solving determinant, expanding along 1st Row


D3 = 50[161500 – 200000]


D3 = – 1925000


Thus by Cramer’s Rule, we have




x = 2


again,




y = 4


and,




z = 11


Thus rates of commission of items A, B and C are 2%, 4% and 11% respectively.


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