If x = a -b, then percentage error in x will be - Vidyadip

MCQ

If $x = a -b,$ then percentage error in $x$ will be

A
$\left( {\frac{{\Delta a}}{a} + \frac{{\Delta b}}{b}} \right) \times 100\,\% $
B
$\left( {\frac{{\Delta a}}{a} - \frac{{\Delta b}}{b}} \right) \times 100\,\% $
✓
$\left( {\frac{{\Delta a}}{a-b} + \frac{{\Delta b}}{a-b}} \right) \times 100\,\% $
D
$\left( {\frac{{\Delta a}}{a-b} - \frac{{\Delta b}}{a-b}} \right) \times 100\,\% $

✓

Answer

Correct option: C.

$\left( {\frac{{\Delta a}}{a-b} + \frac{{\Delta b}}{a-b}} \right) \times 100\,\% $

c
Maximum absolute error is $\Delta a+\Delta b$

Therefore the percentage error $=\frac{\text { absolute error }}{\text { actual error }} \times 100$

$\therefore$ Percentage error $=\left(\frac{\Delta a}{a-b}+\frac{\Delta b}{a-b}\right) \times 100 \%$

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