Two elements A and B combine to form two compounds in which a g of A combines with `b_(1)`, and `b_(2)`, g of B, respectively. According to the law of multiple proportions

Options

A. `b_(1)=b_(2)`
B. `b_(1) ` and `b_(2)` bear a simple whole number ratio
C. `a_(1) ` and `b_(1)` bear whole number ratlo
D. no relation exists between `b_(1)` , and `b_(2)`

Explanation

To solve the question regarding the law of multiple proportions, we can break down the problem step by step.

### Step-by-Step Solution:

1. **Understanding the Law of Multiple Proportions**:
The law of multiple proportions states that when two elements combine to form more than one compound, the masses of one element that combine with a fixed mass of the other element are in a ratio of small whole numbers.

2. **Identifying the Given Information**:
We have two compounds formed by elements A and B. In the first compound, A combines with \( b_1 \) grams of B, and in the second compound, A combines with \( b_2 \) grams of B.

3. **Setting Up the Ratios**:
According to the law of multiple proportions, the ratio of the masses of B that combine with a fixed mass of A should be a simple whole number ratio. Therefore, we can express this as:
\[ \frac{b_1}{b_2} = \frac{n_1}{n_2} \]
where \( n_1 \) and \( n_2 \) are small whole numbers.

4. **Conclusion**:
Since \( b_1 \) and \( b_2 \) represent the masses of B that combine with a fixed mass of A, the law of multiple proportions implies that \( b_1 \) and \( b_2 \) must be in a simple whole number ratio. Thus, we conclude that:
\[ b_1 : b_2 = n_1 : n_2 \]
where \( n_1 \) and \( n_2 \) are integers.

5. **Final Answer**:
Therefore, the correct conclusion according to the law of multiple proportions is that \( b_1 \) and \( b_2 \) are in a simple whole number ratio.