An experiment measures quantities x- y- z and then t is calculated from the data as t - xy2-z3- If percentage errors in x- y and z are respectively 1

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Standard XII

Mathematics

Average Rate of Change

An experiment...

Question

An experiment measures quantities x, y, z and then t is calculated from the data as $t = \frac{x y^{2}}{z^{3}}$ . If percentage errors in x, y and z are respectively 1 %, 3 %, 2 %, then percentage error in t is

10 %

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4 %

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7 %

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13 %

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Solution

The correct option is D 13 %
The given quantity is $t = \frac{x y^{2}}{z^{3}}$
Percentage error in $t$ is given by $\frac{Δ t}{t} \times 100 = 1 \times (\frac{Δ x}{x} \times 100) + 2 (\frac{Δ y}{y} \times 100) + 3 (\frac{Δ z}{z} \times 100)$
$⟹ \frac{Δ t}{t} \times 100 = 1 \times 1 + 2 \times 3 + 3 \times 2 = 13$ %

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An experiment measures quantities x, y, z and then t is calculated from the data as t=xy2z3. If percentage errors in x, y and z are respectively 1 %, 3 %, 2 %, then percentage error in t is

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