A variable w is related to three other variables x, y, z

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A variable w is related to three other variables x, y, z as w = xy/z. The variables are measured with meters of accuracy ± 0.5% reading, ± 1% of full scale value and ± 1.5% reading. The actual readings of the three meters are 80, 20 and 50 with 100 being the full scale value for all three. The maximum uncertainty in the measurement of w will be

1. ± 0.5% rdg
2. ± 5.5% rdg
3. ± 6.7% rdg
4. ± 7.0 rdg

Correct Option: D

Given, w =	xy
	z

Taking log, we get,
log w = log x + log y + log z
By considering only positive error, differentiating with respect to w, we get, for maximum uncertainty

dw	= ±		dx	+	dy	+	dz		× 100
w			x		y		z

= ±		0.4	+	1	+	0.75		× 100
		80		20		50

= 7% of reading