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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
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B
4
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C
5
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D
6
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Solution

The correct option is B 3
The 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  $$3$$%.

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