Assertion : If momentum of a body increases by 50%, its kinetic energy will increase by 125%.
Reason: Kinetic energy is proportional to square of velocity.

Explanation

To solve the problem, we will analyze both the assertion and the reason step by step.

### Step 1: Understand the relationship between momentum and kinetic energy.
The kinetic energy (E) of a body can be expressed in terms of its momentum (p) as follows:
\[ E = \frac{p^2}{2m} \]
where \( m \) is the mass of the body.

### Step 2: Determine the new momentum after a 50% increase.
If the initial momentum is \( p \), then an increase of 50% means the new momentum \( p' \) is:
\[ p' = p + 0.5p = 1.5p \]

### Step 3: Calculate the new kinetic energy using the new momentum.
Substituting \( p' \) into the kinetic energy formula:
\[ E' = \frac{(p')^2}{2m} = \frac{(1.5p)^2}{2m} = \frac{2.25p^2}{2m} = \frac{2.25}{2} \cdot \frac{p^2}{m} = 1.125 \cdot \frac{p^2}{m} \]

### Step 4: Calculate the initial kinetic energy.
The initial kinetic energy \( E \) is:
\[ E = \frac{p^2}{2m} \]

### Step 5: Find the change in kinetic energy.
The change in kinetic energy \( \Delta E \) is:
\[ \Delta E = E' - E = \left(1.125 \cdot \frac{p^2}{m}\right) - \left(\frac{p^2}{2m}\right) \]
To express this in terms of the initial kinetic energy:
\[ \Delta E = \left(1.125 - 0.5\right) \cdot \frac{p^2}{2m} = 0.625 \cdot \frac{p^2}{2m} \]

### Step 6: Express the new kinetic energy in terms of percentage increase.
The new kinetic energy \( E' \) can also be expressed as:
\[ E' = E + \Delta E = E + 0.625E = 1.625E \]
This means the kinetic energy has increased by:
\[ \Delta E = E' - E = 1.625E - E = 0.625E \]
Thus, the percentage increase in kinetic energy is:
\[ \text{Percentage Increase} = \frac{\Delta E}{E} \times 100 = \frac{0.625E}{E} \times 100 = 62.5\% \]

### Conclusion:
The assertion that if momentum increases by 50%, kinetic energy increases by 125% is incorrect. The reason provided is correct as kinetic energy is indeed proportional to the square of velocity.

### Final Answer:
- **Assertion**: Incorrect
- **Reason**: Correct