Question

The percentage error in the measurement of a quantity Z which is related to two other quantities as Z = $x^{-1}{y}^{+1}$ 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

Answer 1

Answer: (A)

3

The quantity is given as $Z=\frac{y}{x}$

$\therefore \frac{\Delta Z}{Z}\times 100=\frac{\Delta x}{x}\times 100+\frac{\Delta y}{y}\times 100$

$⟹\frac{\Delta Z}{Z}\times 100=2+1=3$

Thus percentage error in Z is equal to $3$%.