If the 8-digit number 789x531y is divisible by 72. Then the value of (5x – 3y) is:

The correct option is -1.

To find the value of $(5x-3y)$, we need to determine the digits $x$ and $y$ in the 8-digit number $789x531y$ such that the number is divisible by 72.

A number is divisible by 72 if and only if it is divisible by both 8 and 9, since 8 and 9 are co-prime factors of 72 ($8\times 9=72$).

Step 1: Apply the divisibility rule for 8
A number is divisible by 8 if the number formed by its last three digits is divisible by 8.
The last three digits of our number are $31y$.
We need to find a digit $y$ (where $0\le y\le 9$) such that the 3-digit number $31y$ is divisible by 8.
Let us perform the division:
$310÷8=38$ with a remainder of 6.
Since $38\times 8=304$ and the next multiple of 8 is $39\times 8=312$, the only digit $y$ that makes $31y$ divisible by 8 is:
$y=2$

Step 2: Apply the divisibility rule for 9
A number is divisible by 9 if the sum of its digits is divisible by 9.
Now substituting $y=2$, the 8-digit number becomes $789x5312$.
Let's find the sum of its digits:
Sum $=7+8+9+x+5+3+1+2$
Sum $=35+x$
For this sum to be divisible by 9, $35+x$ must be a multiple of 9.
The nearest multiple of 9 greater than or equal to 35 is 36.
Thus, we set:
$35+x=36$
$x=1$

Step 3: Calculate the value of (5x - 3y)
Substitute the values $x=1$ and $y=2$ into the expression:
$5x-3y=5\left(1\right)-3\left(2\right)$
$5x-3y=5-6$
$5x-3y=-1$