Bina is as many years younger than Abhi as she is older than Chia. Abhi’s age 4 years hence will be equal to Chia’s age 12 years hence. Bina is how many years younger than Abhi?

Options

A. 6
B. 2
C. 3
D. 4

Answer

To solve the problem step by step, let's define the ages of Bina, Abhi, and Chia using variables:

1. Let Bina's age be \( B \).
2. Let Abhi's age be \( A \).
3. Let Chia's age be \( C \).

From the problem statement, we have the following relationships:

- Bina is as many years younger than Abhi as she is older than Chia. This can be expressed mathematically as:
\[ A - B = B - C \]

- Abhi’s age 4 years hence will be equal to Chia’s age 12 years hence. This can be expressed as:
\[ A + 4 = C + 12 \]

Now, we can solve these equations step by step.

### Step 1: Rearranging the first equation
From the first equation \( A - B = B - C \), we can rearrange it to find a relationship between the ages:
\[ A - B + C = B \]
This simplifies to:
\[ A + C = 2B \quad \text{(1)} \]

### Step 2: Rearranging the second equation
From the second equation \( A + 4 = C + 12 \), we can rearrange it to express \( C \) in terms of \( A \):
\[ C = A + 4 - 12 \]
This simplifies to:
\[ C = A - 8 \quad \text{(2)} \]

### Step 3: Substituting equation (2) into equation (1)
Now, substitute \( C \) from equation (2) into equation (1):
\[ A + (A - 8) = 2B \]
This simplifies to:
\[ 2A - 8 = 2B \]
Dividing the entire equation by 2 gives:
\[ A - 4 = B \quad \text{(3)} \]

### Step 4: Finding how many years younger Bina is than Abhi
From equation (3), we see that:
\[ B = A - 4 \]
This means Bina is 4 years younger than Abhi.

### Final Answer
Thus, Bina is **4 years younger than Abhi**.

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