ABCD is a 4-digit number where the sum of A and B is equal to that of the sum of C and D.The sum of A and D is equal to C, and the sum of B and D is twice the sum of A and C. Whatis the sum of the first and the last digit? 

Correct option is B

Let's define the digits of the number ABCD as follows:

• A = First digit
• B = Second digit
• C = Third digit
• D = Fourth digit

We are given the following conditions:

1. A + B = C + D → (Equation 1)
2. A + D = C → (Equation 2)
3. B + D = 2(A + C) → (Equation 3)

Step 1: Express C in terms of A and D

From Equation 2:[C = A + D]Substituting this into Equation 1:

A + B = (A + D) + D

A + B = A + 2D]

​$$B = 2D \quad \text{(Equation 4)}$$​

Step 2: Express B in terms of A

Substituting C = A + D into Equation 3:

B + D = 2(A + (A + D))

B + D = 2(2A + D)

B + D = 4A + 2D

Using B = 2D from Equation 4:

2D + D = 4A + 2D

3D = 4A + 2D

D = 4A

Step 3: Find valid values for A and D

Since A and D are digits (0-9), we need integer values satisfying D = 4A.

The only valid choice is A = 1, which gives D = 4.

Step 4: Find the sum of the first and last digit

A + D = 1 + 4 = 5

Thus, the correct answer is (B) 5.