Question

# The percentage error in the measurement of a quantity Z which is related to two other quantities as Z = $$\displaystyle x^{-1}y^{+1}$$ is due to the percentage error in the measurement of x and y which are 2% and 1% respectively. Find the maximum fractional error in Z (in %).

A
3
B
4
C
5
D
6

Solution

## The correct option is B 3The quantity is given as      $$Z = \dfrac{y}{x}$$$$\therefore \dfrac{\Delta Z}{Z} \times 100 = \dfrac{\Delta x}{x} \times 100 + \dfrac{\Delta y}{y} \times 100$$$$\implies \dfrac{\Delta Z}{Z} \times 100 = 2+1 = 3$$Thus percentage error in Z is equal to  $$3$$%.Maths

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