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12th Business Maths Weekly Test - 3 ( Applications of Matrices and Determinants )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Weekly Test - 3 ( Applications of Matrices and Determinants )-Aug 2020

Time : 1.00 Hours

Part - A

Generic 2 - Answer All Question

The price of three commodities X,Y and Z are x,y and z respectively Mr.Anand
purchases 6 units of Z and sells 2 units of X and 3 units of Y. Mr.Amar purchases a
unit of Y and sells 3 units of X and 2units of Z. Mr.Amit purchases a unit of X and
sells 3 units of Y and a unit of Z. In the process they earn `5,000/-, `2,000/- and
`5,500/- respectively Find the prices per unit of three commodities by rank method.

Two types of soaps A and B are in the market. Their present market shares are 15% for A and 85% for B. Of those who bought A the previous year, 65% continue to buy it again while 35% switch over to B. Of those who bought B the previous year, 55% buy it again and 45% switch over to A. Find their market shares after one year and when is the equilibrium reached?

At marina two types of games viz., Horse riding and Quad Bikes riding are available
on hourly rent. Keren and Benita spent Rs 780 and Rs 560 during the month of May.

Name Number of hours Total amount spent
(in Rs)

Horse Riding Quad Bike Riding

Keren 3 4 780

Benita 2 3 560

Find the hourly charges for the two games (rides). (Use determinant method).

Find k if the equations x+y+z=1,3x−y−z=4,x+5y+5z=k are inconsistent.

Solve the equations x+2y+z=7,2x−y+2z=4,x+y−2z = −1 by using Cramer’s rule

A total of Rs 8,600 was invested in two accounts. One account earned \(4\frac { 3 }{ 4 } %\)% annual
interest and the other earned \(6\frac { 1 }{ 2 } %\)% annual interest. If the total interest for one year
was Rs 431.25, how much was invested in each account? (Use determinant method).

Show that the equations5x+3y+7z=4,3x+26y+2z=9,7x+2y+10z =5 are consistent and solve them by rank method.

Two products A and B currently share the market with shares 50% and 50% each
respectively. Each week some brand switching takes place. Of those who bought A
the previous week, 60% buy it again whereas 40% switch over to B. Of those who
bought B the previous week, 80% buy it again where as 20% switch over to A. Find
their shares after one week and after two weeks. If the price war continues, when is
the equilibrium reached?

The subscription department of a magazine sends out a letter to a large mailing list inviting subscriptions for the magazine. Some of the people receiving this letter
already subscribe to the magazine while others do not. From this mailing list, 60% of those who already subscribe will subscribe again while 25% of those who do
not now subscribe will subscribe. On the last letter it was found that 40% of those receiving it ordered a subscription. What percent of those receiving the current
letter can be expected to order a subscription?

A commodity was produced by using 3 units of labour and 2 units of capital, the
total cost is Rs 62. If the commodity had been produced by using 4 units of labour
and one unit of capital, the cost is Rs 56. What is the cost per unit of labour and
capital? (Use determinant method).

A total of Rs 8,500 was invested in three interest earning accounts. The interest rates were 2%, 3% and 6% if the total simple interest for one year was Rs 380 and the amount ,invested at 6% was equal to the sum of the amounts in the other two accounts, then how much was invested in each account? (use Cramer’s rule).

Find the rank of the matrix A =\(\left( \begin{matrix} 1 & -3 \\ 9 & 1 \end{matrix}\begin{matrix} 4 & 7 \\ 2 & 0 \end{matrix} \right) \)

Solve the following equation by using Cramer’s rule
5x + 3y = 17; 3x + 7y = 31

A salesman has the following record of sales during three months for three items
A,B and C, which have different rates of commission.

Months Sales of units Total commission drawn (in Rs)

A B C

January 90 100 20 800

February 130 50 40 900

March 60 100 30 850

Show that the following system of equations have unique solution:
x+y+z=3,x+2y+3z=4,x+4y+9z = 6 by rank method.

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