Question

In a manufacturing plant x,y,z amounts of output are produced by three different brands of equipment. If the output capacity of the equipment which produces x amount of output is increased by %20,and the other two equipments capacity gets reduced by %5,the total output remains unchanged.What is the relationship between x,y and z ?

Answer 1

Let the quantities produced by 3 equipments are = X, Y and Z

Total quantity produced = X + Y + Z

If output of X increases by 20% , revised output = 1.20.X

If output of Y reduces by 5%, revised output = 0.95.Y

If output of Z reduces by 5% , revised output = 0.95.Z

Total revised quantity = 1.20.X + 0.95.Y + 0.95Z

Since total output remains unchanged ,

X+ Y + Z = 1.20.X + 0.95Y + 0.95.Z

Or, ( X + Y+Z) - ( 1.20X + 0.95.Y + 0.95.Z) = 0

Or, 0.05.Y + 0.05.Z - 0.20.X = 0

Or, Y + Z - 4.X = 0

RELATIONSHIP BETWEEN X, Y AND Z WILL BE Y + Z - 4.X = 0