Q18 of 75 Page 8

Two schools P and Q want to award their selected students on the values of Discipline, Politeness and Punctuality. The school P wants to award ₹x each, ₹y each and ₹z each for the three respectively values to its 3, 2 and 1 students with a total award money of ₹1,000. School Q wants to spend ₹1,500 to award its 4,1 and 3 students on the respective values (by giving the same award money for three values as before.) If the total amount of awards for one prize on each value is ₹600, using matrices, find the award money for each value, Apart on each value is ₹600, using matrices, find the award money for each value, Apart from the above three values, suggest one more value for awards.

x,y and z be the prize amount per student for Discipline, Politeness and Punctuality respectively.


3x + 2y + z = 1000


4x + y + 3z = 1500


x + y + z = 600


These three equations can be written as



A X = B


|A| = 3(1 – 3) – 2(4 – 3) + 1(4 – 1)


= 3(– 2) – 2(1) + 1(3)


= – 6 – 2 + 3


= – 5


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


C11 = (– 1)1 + 1 (1 – 3) = – 2


C12 = (– 1)1 + 2 (4 – 3) = – 1


C13 = (– 1)1 + 3 (4 – 1) = 3


C21 = (– 1)2 + 1 (2 – 1) = – 1


C22 = (– 1)2 + 2 (3 – 1) = 2


C23 = (– 1)2 + 3 (3 – 2 ) = – 1


C31 = (– 1)3 + 1 (6 – 1) = 5


C32 = (– 1)3 + 2 (9 – 4) = – 5


C33 = (– 1)3 + 3 (3 – 8) = – 5


Adj A =


X = A – 1 B =


X =


X =


X =


=


Hence, x = 100, y = 200 and z = 300


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16

Two factories decided to award their employees for three values of (a) adaptable to new techniques, (b) careful and alert in difficult situations and (c) keeping calm in tense situations, at the rate of ₹x, ₹y and ₹z per persons respectively. The first factory decided to honour respectively 2, 4 and 3 employees with total prize money of ₹29000. The second factory decided to honour respectively 5, 2 and 3 employees with the prize money of ₹30500. If the three prizes per person together cost ₹9500, then

i. represent the above situation by a matrix equation and form linear equations using matrix multiplication.


ii. Solve these equations using matrices.


iii. Which values are reflected in the questions?

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Two schools P and Q want to award their selected students on the values of Tolerance, Kindness and Leadership. The school P want to award ₹x each, ₹y each and ₹z each for the three respective values to 3,2 and 1 students respectively with total award money of ₹2,200. School Q wants to spend ₹3,100 to award its 4,1 and 3 students on the respective values (by giving the same award money to the three values as school P). If the total amount of award for one prize on each values is ₹1,200, using matrices, find the award money for each value. Apart from these three values, suggest one more value which should be considered for the award

 20

A total amount of ₹7000 is deposited in three different saving bank accounts with annual interest rates of 5%, 8% and respectively. The total annual interest from these three accounts is ₹550. Equal amounts have been deposited in the 5% and 8% savings accounts. Find the amount deposited in each of the three accounts, with the help of matrices.