1. Given relation:

$Q=\frac{a^4 b^3}{c^2}$

2. For multiplication/division with powers, the maximum percentage error is the sum of absolute fractional errors multiplied by the powers:

$\frac{\Delta Q}{Q}\times 100 = 4\left(\frac{\Delta a}{a}\times 100\right)+3\left(\frac{\Delta b}{b}\times 100\right)+2\left(\frac{\Delta c}{c}\times 100\right)$

3. Substitute the given percentage errors:

• Error in $a = 3\%$
• Error in $b = 4\%$
• Error in $c = 5\%$

So,

$\%\text{ error in }Q = 4(3)+3(4)+2(5)$

4. Calculate:

$=12+12+10=34\%$

5. Therefore, the percentage error in $Q$ is

$\boxed{34\%}$

6. Option check:

• A: $43\%$ ✗
• B: $34\%$ ✓
• C: $66\%$ ✗
• D: $14\%$ ✗

Hence, the correct option is B.