There are 2 teams A and B. If 3 people are shifted from Team A to Team B, then Team B has thrice the number of members than Team A. If 2 people are shifted from Team B to Team A, then Team B has double the number of members than Team A. How many members does team B have originally ?

Options

A. 15
B. 18
C. 42
D. 45

Answer

Let's denote the number of members in Team A as \( a \) and the number of members in Team B as \( b \).

### Step 1: Set up the equations based on the problem statement.

1. According to the first condition, if 3 people are shifted from Team A to Team B, then Team B has three times the number of members than Team A. This can be expressed as:
\[ b + 3 = 3(a - 3) \]

2. According to the second condition, if 2 people are shifted from Team B to Team A, then Team B has double the number of members than Team A. This can be expressed as:
\[ b - 2 = 2(a + 2) \]

### Step 2: Simplify the equations.

1. From the first equation:
\[ b + 3 = 3a - 9 \]
Rearranging gives:
\[ b = 3a - 12 \quad \text{(Equation 1)} \]

2. From the second equation:
\[ b - 2 = 2a + 4 \]
Rearranging gives:
\[ b = 2a + 6 \quad \text{(Equation 2)} \]

### Step 3: Solve the equations simultaneously.

Now we have two equations:
1. \( b = 3a - 12 \)
2. \( b = 2a + 6 \)

Setting them equal to each other:
\[ 3a - 12 = 2a + 6 \]

### Step 4: Isolate \( a \).

Subtract \( 2a \) from both sides:
\[ 3a - 2a - 12 = 6 \]
This simplifies to:
\[ a - 12 = 6 \]
Adding 12 to both sides gives:
\[ a = 18 \]

### Step 5: Substitute \( a \) back to find \( b \).

Now substitute \( a = 18 \) back into either Equation 1 or Equation 2. We'll use Equation 2:
\[ b = 2(18) + 6 \]
Calculating gives:
\[ b = 36 + 6 = 42 \]

### Conclusion

Thus, the number of members in Team B originally is \( \boxed{42} \).