The relative reactivity of `1^(@) : 2^(@) : 3^(@) H's` to brominate is `1:82:1600`, respectively. In the reaction
`CH_(3)-underset("Excess")overset(CH_(3))overset(|)(CH)CH_(3)+Br_(2)overset(hv)rarrCH_(3)underset((A))underset(Br)underset(|)overset(CH_(3))overset(|)(C) CH_(3)+CH_(3)underset((B))overset(CH_(3))overset(|)CHCH_(2)Br`
the percentage yield of the products `(A)` and `(B)` are expected to be

Answer

To solve the problem, we need to calculate the percentage yield of products (A) and (B) based on the given relative reactivity of the hydrogen atoms and the number of equivalent hydrogens in the reaction.

### Step-by-Step Solution:

1. **Identify the Relative Reactivity**:
- The relative reactivity of the hydrogen atoms is given as:
- 1° H: 1
- 2° H: 82
- 3° H: 1600

2. **Determine the Relative Amount of Product A**:
- Product (A) is formed by replacing a 3° hydrogen.
- The relative reactivity of 3° H is 1600.
- The number of equivalent 3° hydrogens in the structure is 1 (since there is one 3° hydrogen in the given structure).
- Therefore, the relative amount of product A:
\[ \text{Relative amount of A} = \text{Relative reactivity of 3° H} \times \text{Number of equivalent 3° H} = 1600 \times 1 = 1600 \]

3. **Determine the Relative Amount of Product B**:
- Product (B) is formed by replacing 1° hydrogens.
- The relative reactivity of 1° H is 1.
- The number of equivalent 1° hydrogens in the structure is 9 (3 from each of the three methyl groups).
- Therefore, the relative amount of product B:
\[ \text{Relative amount of B} = \text{Relative reactivity of 1° H} \times \text{Number of equivalent 1° H} = 1 \times 9 = 9 \]

4. **Calculate the Total Relative Amount**:
- Total relative amount = Relative amount of A + Relative amount of B
\[ \text{Total relative amount} = 1600 + 9 = 1609 \]

5. **Calculate the Percentage Yield of Product A**:
- The formula for percentage yield is:
\[ \text{Percentage yield of A} = \left( \frac{\text{Relative amount of A}}{\text{Total relative amount}} \right) \times 100 \]
- Substituting the values:
\[ \text{Percentage yield of A} = \left( \frac{1600}{1609} \right) \times 100 \approx 99.4\% \]

6. **Calculate the Percentage Yield of Product B**:
- Using the same formula:
\[ \text{Percentage yield of B} = \left( \frac{\text{Relative amount of B}}{\text{Total relative amount}} \right) \times 100 \]
- Substituting the values:
\[ \text{Percentage yield of B} = \left( \frac{9}{1609} \right) \times 100 \approx 0.6\% \]

### Final Answers:
- Percentage yield of product (A) = **99.4%**
- Percentage yield of product (B) = **0.6%**