If 11-digit number `543247 x 968y` is divisible by 90, then the value of `(4x+5y)`.

Options

A. 24
B. 21
C. 25
D. 16

Answer

To determine the value of \(4x + 5y\) for the 11-digit number \(543247 \times 968y\) that is divisible by 90, we need to follow these steps:

### Step 1: Understand the divisibility rules
A number is divisible by 90 if it is divisible by both 9 and 10.

### Step 2: Check divisibility by 10
For a number to be divisible by 10, its last digit must be 0. Therefore, we have:
\[ y = 0 \]

### Step 3: Check divisibility by 9
Next, we need to ensure that the number is divisible by 9. A number is divisible by 9 if the sum of its digits is divisible by 9.

### Step 4: Calculate the sum of the digits
Now we calculate the sum of the digits in \(543247968y\) with \(y = 0\):
- The digits are: \(5, 4, 3, 2, 4, 7, 9, 6, 8, 0\)
- We calculate the sum:
\[ 5 + 4 + 3 + 2 + 4 + 7 + 9 + 6 + 8 + 0 = 48 \]

### Step 5: Check if the sum is divisible by 9
Now we check if 48 is divisible by 9:
- The sum of the digits of 48 is \(4 + 8 = 12\), and \(12\) is not divisible by \(9\).

### Step 6: Adjust for \(x\)
Since \(y = 0\), we need to find \(x\) such that the total sum \(48 + x\) is divisible by 9. We check:
- \(48 + x \equiv 0 \mod 9\)
- \(48 \mod 9 = 3\), so we need:
\[ 3 + x \equiv 0 \mod 9 \implies x \equiv 6 \mod 9 \]
Thus, \(x\) can be \(6\) (since \(x\) must be a single digit).

### Step 7: Calculate \(4x + 5y\)
Now we substitute \(x = 6\) and \(y = 0\) into \(4x + 5y\):
\[ 4x + 5y = 4(6) + 5(0) = 24 + 0 = 24 \]

### Final Answer
The value of \(4x + 5y\) is:
\[ \boxed{24} \]