If `a= 8 pm 0.08 and b = 6pm 0.06`, let x = a+ b, y = a-b, z=ab.
The correct order of % error in x, y and z is

Answer

N/a

Explanation

x,y, z are in A.P.
`rArr" "2y=x+z " ...(1)"`
a is the A.M. of x and y
`rArr" "a=(x+y)/(2)" ...(2)"`
b is the A.M. of y and z
`rArr" "b=(y+z)/(2)" ...(3)"`
Adding eqs. (2) and (3), we get
`a+b=(x+y)/(2)+(y+z)/(2)`
`=(x+y+y+z)/(2)`
`=(x+z+2y)/(2)`
`(2y+2y)/(2)=2y" [From eq. (1)]"`
`rArr" "(a+b)/(2)=y`
Therefore, y is the arithmetic mean of a and b.