A traveller goes from City P to Q at 24 km/h in 5 hours. To complete it in 3 hours, by how much should speed increase?

The correct option is 16 km/h.

To find the required increase in speed, we first need to determine the total distance between City P and City Q.

Step 1: Calculate the total distance.
Distance is given by the formula:
$\text{Distance}=\text{Speed}\times \text{Time}$

Given initial speed = 24 km/h and initial time = 5 hours:
$\text{Distance}=24\times 5=120\text{km}$

Step 2: Calculate the required new speed.
To cover the same distance of 120 km in 3 hours, the new speed must be:
$\text{New Speed}=\frac{\text{Distance}}{\text{Time}}$

$\text{New Speed}=\frac{120}{3}=40\text{km/h}$

Step 3: Calculate the increase in speed.
$\text{Increase in Speed}=\text{New Speed}-\text{Initial Speed}$

$\text{Increase in Speed}=40-24=16\text{km/h}$

Therefore, the traveller should increase the speed by 16 km/h.