An experiment measured quantity a, b, c and then x is calculated from `x = ab^(2)//c^(3)`. If the percentage error in a, b, c are `pm` 1%, `pm` 3% and `pm` 2% respectively, the percentage error in x can be,

Options

A. `13%`
B. `12%`
C. `11%`
D. `10%`

Answer

A

Explanation

Here, `(Deltaa)/(a)xx100 pm 1%, (Deltab)/(b)xx100=pm 3%, (Deltac)/(c )xx100=pm 2%`
`x=(ab^(2))/(c^(3))`
Maximum percentage error in x is `(Deltax)/(x)xx100=(Deltaa)/(a)xx100+2(Deltab)/(b)xx100+3(Deltac)/(c )xx100=1+(2xx3)+(3xx2)=13%`
Maximum percentage error is x is `13%`.