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 value of x (in Rs.) is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 4000
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):
\(3x = 12000\)
\(x = 4000\)
Check: z = 3000 and y = 5000, and 4(4000) + 3(5000) + 2(3000) = 37000.