A physical quantity Q is found to depend on quantities a, b, c by...

Given quantity is $Q = \dfrac{{a}^{4}{b}^{3}}{{c}^{2}}$.

The relative error in measuring $Q$ is given by

$\dfrac{\DeltaQ}{Q} = 4\dfrac{\Deltaa}{a} + 3\dfrac{\Deltab}{b} + 2\dfrac{\Deltac}{c} . . . \left(1\right)$

Hence, the required percentage error is given by

\begin{cases}\dfrac{\DeltaQ}{Q} \times 100 & = & 4\left(\dfrac{\Deltaa}{a} \times 100\right) + 3\left(\dfrac{\Deltab}{b} \times 100\right) + 2\left(\dfrac{\Deltac}{c} \times 100\right) \\ & = & 4 \times 3 % + 3 \times 4 % + 2 \times 5 % \\ & = & 12 % + 12 % + 10 % \\ & = & 34 %\end{cases}