Two institutions decided to award their employees for resourcefulness, competence and determination in the form of prizes at the rate of Rs. x, Rs. y, Rs. z respectively per person. The first institution decided to award respectively 4, 3 and 2 employees with total prize money Rs. 37,000 and second institution decided to award respectively 5, 3 and 4 employees with the total prize money of Rs. 47,000 for resourcefulness, competence and determination. All the prizes per person together amount to Rs. 12,000.
The values of y and z (in Rs.) are:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 5000, 3000
The information gives the equations
\(4x + 3y + 2z = 37000 \quad (1)\)
\(5x + 3y + 4z = 47000 \quad (2)\)
\(x + y + z = 12000 \quad (3)\)
Eliminate y by subtracting 3 × (3) from (1) and from (2):
\(x - z = 1000 \quad (4)\)
\(2x + z = 11000 \quad (5)\)
Adding (4) and (5):
\(3x = 12000\)
\(x = 4000\)
Then
\(z = x - 1000 = 3000\)
\(y = 12000 - 4000 - 3000 = 5000\)
So y = Rs. 5000 and z = Rs. 3000.