Assertion : On simplifying `10/11 xx (-14/5) +10/11 xx (-8/5)` we get `-4`.
Reason : While adding rational numbers with same denominators, we add the numerators and denominator separately.

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 assertion and reason question, we will simplify the expression step by step.

### Step-by-Step Solution:

1. **Write down the expression**:
\[ \frac{10}{11} \times \left(-\frac{14}{5}\right) + \frac{10}{11} \times \left(-\frac{8}{5}\right) \]

2. **Calculate the first term**:
\[ \frac{10}{11} \times \left(-\frac{14}{5}\right) = \frac{10 \times -14}{11 \times 5} = \frac{-140}{55} \]

3. **Calculate the second term**:
\[ \frac{10}{11} \times \left(-\frac{8}{5}\right) = \frac{10 \times -8}{11 \times 5} = \frac{-80}{55} \]

4. **Combine the two fractions**:
Since both fractions have the same denominator, we can add the numerators directly:
\[ \frac{-140}{55} + \frac{-80}{55} = \frac{-140 - 80}{55} = \frac{-220}{55} \]

5. **Simplify the result**:
\[ \frac{-220}{55} = -4 \]

### Conclusion:
The assertion that simplifying the expression gives \(-4\) is correct.

### Reason Analysis:
The reason states that while adding rational numbers with the same denominators, we add the numerators and denominators separately. This is incorrect because we only add the numerators when the denominators are the same.

### Final Answer:
- The assertion is true, but the reason is false. Therefore, the correct option is that the assertion is correct, but the reason is incorrect.

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