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Q.

If x = a - b, then the maximum percentage error in the measurement of x will be

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a

$(\frac{Δa}{b - a} + \frac{Δb}{a - b}) \times 100 %$

b

$(\frac{Δ a}{a - b} - \frac{Δ b}{a - b}) \times 100 %$

c

$(\frac{Δ a}{a} - \frac{Δ b}{b}) \times 100 %$

d

$(\frac{Δ a + Δ b}{a - b}) \times 100 %$

answer is A.

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Detailed Solution

Maximum absolute error in addition and subtraction is $Δ a + Δ b .$ Now work out the relative error and finally the percentage error.

$\frac{Δ x}{x} \times 100 = (\frac{Δ a + Δ b}{a - b}) \times 100 %$

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If x = a - b, then the maximum percentage error in the measurement of x will be