Q. 45

# Two schools A and B want to award their selected students on the values of sincerity, truthfulness and helpfulness. The school A wants 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 ₹ 1,600. School B wants to spend ₹ 2,300 to award its 4, 1 and 3 students on the respective values (by giving the same award money to the three values as before). If the total amount of award for one prize on each value is ₹ 900, using matrices, find the award money for each value. Apart from these three values, suggest one more value which should be considered for award.HINT: By the given data, we have

Let the amount x, y and z be considered for sincerity, truthfulness and helpfulness.

According to the questions,

3x + 2y + z = 1600

4x + y + 3z = 2300

X + y + z = 900

Converting into the matrix form

AX = B

R1 – 3R3

R2 – 4R3

2R2 - R1

Converting back into the equations we get

- y - 2z = - 1100

- 5y = - 1500

X + y + z = 900

Y = 300

- 300 - 2z = - 1100

- 2z = - 800

Z = 400

X + 300 + 400 = 900

X = 900 - 700

X = 200

₹ 200 for sincerity, ₹ 300 for truthfulness and ₹ 400 for helpfulness. One more value may be like honesty, kindness, etc.

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