Q. If $x = a - b$, then the maximum percentage error in the measurement of $x$ will be
A) $\left( \frac{\mathrm{\Delta}a + \mathrm{\Delta}b}{a - b} \right) \times 100\%$
B) $\left( \frac{\mathrm{\Delta}a}{a} - \frac{\mathrm{\Delta}b}{b} \right) \times 100\%$
C) $\left( \frac{\mathrm{\Delta}a}{a - a} + \frac{\mathrm{\Delta}b}{a - b} \right) \times 100\%$
D) $\left( \frac{\mathrm{\Delta}a}{a - a} - \frac{\mathrm{\Delta}b}{a - b} \right) \times 100\%$
Explanation
Maximum absolute error is $\Delta a + \Delta b$. Now work out the relative error ad finally the percentage error.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.