Assertion: If Ajay spent `2(1)/(6)` hours in reading a storybook and spent `(1)/(3)` of an hour in playing computer game, then the total time spent by Ajay is 2 hours.
Reason: Mixed fractions can be written either as a whole part plus a proper fraction or entirely as an improper fraction.

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 determine whether the assertion about Ajay's total time spent is true or false, and also understand the reason provided about mixed fractions.

### Step-by-Step Solution:

1. **Convert the Mixed Fraction to an Improper Fraction:**
- Ajay spent \(2 \frac{1}{6}\) hours reading.
- To convert this mixed fraction to an improper fraction:
\[ 2 \frac{1}{6} = \frac{(2 \times 6) + 1}{6} = \frac{12 + 1}{6} = \frac{13}{6} \]

2. **Convert the Playing Time to an Improper Fraction:**
- Ajay spent \(\frac{1}{3}\) hours playing computer games. This is already a proper fraction.

3. **Find a Common Denominator:**
- The denominators are 6 and 3. The least common multiple (LCM) of 6 and 3 is 6.

4. **Convert \(\frac{1}{3}\) to a Fraction with a Denominator of 6:**
- To convert \(\frac{1}{3}\) to have a denominator of 6:
\[ \frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6} \]

5. **Add the Two Fractions:**
- Now we can add \(\frac{13}{6}\) and \(\frac{2}{6}\):
\[ \frac{13}{6} + \frac{2}{6} = \frac{13 + 2}{6} = \frac{15}{6} \]

6. **Convert the Improper Fraction Back to a Mixed Fraction:**
- To convert \(\frac{15}{6}\) back to a mixed fraction:
\[ 15 \div 6 = 2 \quad \text{(whole part)} \]
- The remainder is \(15 - (6 \times 2) = 3\).
- Thus, \(\frac{15}{6} = 2 \frac{3}{6}\), which simplifies to \(2 \frac{1}{2}\).

7. **Conclusion:**
- The total time spent by Ajay is \(2 \frac{1}{2}\) hours, which is more than 2 hours. Therefore, the assertion that Ajay spent a total of 2 hours is **false**.

### Final Evaluation:
- **Assertion:** False (Ajay spent \(2 \frac{1}{2}\) hours, not 2 hours).
- **Reason:** True (Mixed fractions can be expressed as a whole number plus a proper fraction or as an improper fraction).