A person travelled 80 km in 6 hours. If the person travelled the first part with a uniform speed of 10 kmph and the remaining part with a uniform speed of 18 kmph. What percentage of the total distance is travelled at a uniform speed of 10 kmph?

The correct option is 43.75.

Step-by-step derivation:

Let us denote the distance travelled during the first part (at a uniform speed of 10 kmph) as $d_1$ km and the distance travelled during the remaining part (at a uniform speed of 18 kmph) as $d_2$ km.

Since the total distance travelled is 80 km, we can write the first equation as:
$$d_1+d_2=80$$
From this, we can express $d_2$ in terms of $d_1$:
$$d_2=80-d_1$$

The total time taken to travel the entire distance is 6 hours. Time is given by the formula:
$$\text{Time}=\frac{\text{Distance}}{\text{Speed}}$$
Therefore, the sum of the times for both parts of the journey is:
$$\frac{d_1}{10}+\frac{d_2}{18}=6$$

Substitute $d_2=80-d_1$ into the time equation:
$$\frac{d_1}{10}+\frac{80-d_1}{18}=6$$

To eliminate the denominators, we multiply the entire equation by the Least Common Multiple (LCM) of 10 and 18, which is 90:
$$9d_1+5(80-d_1)=6\times 90$$

Simplify and solve for $d_1$:
$$9d_1+400-5d_1=540$$
$$4d_1=540-400$$
$$4d_1=140$$
$$d_1=35\text{km}$$

Now, we calculate the percentage of the total distance travelled at the uniform speed of 10 kmph:
$$\text{Percentage}=\left(\frac{d_1}{\text{Total Distance}}\right)\times 100$$
$$\text{Percentage}=\left(\frac{35}{80}\right)\times 100$$
$$\text{Percentage}=0.4375\times 100=43.75\%$$