If we write 45 as sum of four numbers so that when 2 is added to first number, 2 subtracted from second number, third multiplied by 2 and fourth divided by 2. we get the same result, then the four numbers are :

Options

A. 1, 8, 15, 21
B. 8, 12, 5, 20
C. 8, 12, 10, 15
D. 2, 12, 5, 26

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define the Variables
Let the four numbers be \( a, b, c, \) and \( d \).

### Step 2: Set Up the Equation
According to the problem, the sum of the four numbers is:
\[ a + b + c + d = 45 \]

### Step 3: Set Up the Conditions
The problem states that:
1. When 2 is added to the first number: \( a + 2 \)
2. When 2 is subtracted from the second number: \( b - 2 \)
3. When the third number is multiplied by 2: \( 2c \)
4. When the fourth number is divided by 2: \( \frac{d}{2} \)

All these expressions are equal:
\[ a + 2 = b - 2 = 2c = \frac{d}{2} \]

### Step 4: Express \( b, c, \) and \( d \) in terms of \( a \)
From the first equality \( a + 2 = b - 2 \):
\[ b = a + 4 \]

From the second equality \( a + 2 = 2c \):
\[ c = \frac{a + 2}{2} \]

From the third equality \( a + 2 = \frac{d}{2} \):
\[ d = 2(a + 2) = 2a + 4 \]

### Step 5: Substitute Back into the Sum Equation
Now substitute \( b, c, \) and \( d \) back into the sum equation:
\[ a + (a + 4) + \left(\frac{a + 2}{2}\right) + (2a + 4) = 45 \]

### Step 6: Simplify the Equation
Combine like terms:
\[ a + a + 4 + \frac{a + 2}{2} + 2a + 4 = 45 \]
\[ 4a + 8 + \frac{a + 2}{2} = 45 \]

Multiply the entire equation by 2 to eliminate the fraction:
\[ 2(4a + 8) + (a + 2) = 90 \]
\[ 8a + 16 + a + 2 = 90 \]
\[ 9a + 18 = 90 \]

### Step 7: Solve for \( a \)
Subtract 18 from both sides:
\[ 9a = 72 \]
Divide by 9:
\[ a = 8 \]

### Step 8: Find \( b, c, \) and \( d \)
Now substitute \( a \) back to find \( b, c, \) and \( d \):
- \( b = a + 4 = 8 + 4 = 12 \)
- \( c = \frac{a + 2}{2} = \frac{8 + 2}{2} = \frac{10}{2} = 5 \)
- \( d = 2a + 4 = 2(8) + 4 = 16 + 4 = 20 \)

### Final Answer
The four numbers are:
\[ \boxed{8, 12, 5, 20} \]