A person travels from X to Y at a speed of 50 km/hr and returns from Y to X by increasing his speed by 50%. His average speed during the journey is.

The correct option is 60 km/hr.

Let us break down the solution step-by-step to understand how to find the average speed of the entire journey.

Step 1: Determine the speed for both parts of the journey.
The person travels from X to Y at a speed of 50 km/hr. Let this forward speed be denoted by:
$v_1=50\text{km/hr}$
On the return journey from Y to X, the person increases their speed by 50%.
An increase of 50% on the initial speed of 50 km/hr is calculated as:
$\text{Increase}=50\%\text{of}50=\frac{50}{100}\times 50=25\text{km/hr}$
Therefore, the return speed (let's call it $v_2$) is:
$v_2=50+25=75\text{km/hr}$

Step 2: Understand the concept of Average Speed for equal distances.
Since the distance from X to Y is the same as the distance from Y to X, the journey consists of two equal distance segments traveled at different speeds.
When equal distances are covered at two different speeds $v_1$ and $v_2$, the average speed is given by the harmonic mean of the speeds:
$\text{Average Speed}=\frac{2v_1{v}_2}{v_1+v_2}$

Step 3: Calculate the average speed.
Substituting the values $v_1=50\text{km/hr}$ and $v_2=75\text{km/hr}$ into the formula:
$\text{Average Speed}=\frac{2\times 50\times 75}{50+75}$
$\text{Average Speed}=\frac{7500}{125}$
$\text{Average Speed}=60\text{km/hr}$

Thus, the average speed of the person during the entire journey is 60 km/hr.