Assertion : The H.C.F. of two numbers is 28 and their L.C.M. is 336. If one number is 112, then the other number is 84.
Reason: The product of two numbers is equal to the H.C.F. and L.C.M of the numbers.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If assertion is false but reason is true.

Answer

To solve the problem, we need to verify the assertion and the reason provided in the question.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
The assertion states that the H.C.F. (Highest Common Factor) of two numbers is 28, their L.C.M. (Lowest Common Multiple) is 336, and if one number is 112, then the other number is 84.

2. **Using the Relationship between H.C.F. and L.C.M.**:
The product of two numbers is equal to the product of their H.C.F. and L.C.M. This can be expressed as:
\[ \text{Number 1} \times \text{Number 2} = \text{H.C.F.} \times \text{L.C.M.} \]

3. **Substituting the Known Values**:
We know one number is 112, H.C.F. is 28, and L.C.M. is 336. Let's denote the second number as \( x \). Therefore, we can write:
\[ 112 \times x = 28 \times 336 \]

4. **Calculating the Right Side**:
First, calculate \( 28 \times 336 \):
\[ 28 \times 336 = 9408 \]

5. **Setting Up the Equation**:
Now, we have the equation:
\[ 112 \times x = 9408 \]

6. **Solving for \( x \)**:
To find \( x \), divide both sides by 112:
\[ x = \frac{9408}{112} \]
Performing the division:
\[ x = 84 \]

7. **Conclusion**:
The other number is indeed 84, confirming the assertion is correct.

8. **Understanding the Reason**:
The reason states that the product of two numbers is equal to the H.C.F. and L.C.M. of the numbers. This is a true statement and supports the assertion.

### Final Conclusion:
Both the assertion and the reason are true, and the reason correctly explains the assertion.