Two elements A and B combine to form compound X and Y. For the fix mass of A, masses of B contained for the compounds X and Y are in 3:7 ratio. If in compound X, 4gm of A combines with 12gm B, then in compound Y, 8gm of A will combine with… gm of B.

Options

A. 24
B. 56
C. 28
D. 8

Answer

To solve the problem step by step, we can follow this approach:

### Step 1: Understand the given information
We know that two elements A and B combine to form compounds X and Y. The mass of B in compounds X and Y for a fixed mass of A is in the ratio of 3:7. We also know that in compound X, 4 grams of A combines with 12 grams of B.

### Step 2: Determine the mass of B for compound Y
Since the ratio of the masses of B in compounds X and Y is given as 3:7, we can set up a relationship based on the mass of B in compound X.

Let the mass of B in compound X be represented as 3k and in compound Y as 7k, where k is a constant.

From the information given:
- In compound X, 4 grams of A combines with 12 grams of B.

Thus, we can equate the mass of B in compound X:
\[ 3k = 12 \text{ grams} \]

### Step 3: Solve for k
To find the value of k, we can rearrange the equation:
\[ k = \frac{12}{3} = 4 \]

### Step 4: Calculate the mass of B in compound Y
Now that we have the value of k, we can find the mass of B in compound Y:
\[ \text{Mass of B in compound Y} = 7k = 7 \times 4 = 28 \text{ grams} \]

### Step 5: Determine the mass of B when the mass of A is 8 grams
The problem states that in compound Y, 8 grams of A will combine with a certain mass of B. Since the ratio of B to A remains constant, we can use the ratio derived from compound X to find the corresponding mass of B.

In compound X, the ratio of A to B is:
\[ \frac{4 \text{ grams of A}}{12 \text{ grams of B}} = \frac{1}{3} \]

Now, we can apply the same ratio to find the mass of B when we have 8 grams of A in compound Y:
\[ \text{Mass of B} = \left( \frac{12 \text{ grams of B}}{4 \text{ grams of A}} \right) \times 8 \text{ grams of A} = 3 \times 8 = 24 \text{ grams} \]

### Final Answer
Thus, in compound Y, 8 grams of A will combine with **28 grams of B**.

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