If the seven digit number 54x29y6 (x > y)is divisible by 72, what is the value of (2x + 3y)?

Given, 7-digit number 54x29y6 is divisible by 72 then the number must be divisible by 8 and 9, and x>y

If it is divisible by 8 then, the last three digits should be divisible by 8

$$=$$> 9y6 is divisible by 8

$$=$$> The possible values of y are 3,7

$$=$$> y=3 or y=7

If it is divisible by 9 then, sum of the digits should be divisble by 9

$$=$$> 5+4+x+2+9+y+6 = multiple of 9

$$=$$> 26+x+y = multiple of 9

Case 1: if y=3

$$=$$> 26+x+3 = multiple of 9

$$=$$> 29+x = multiple of 9

$$=$$> The possible value of x is 7

$$=$$> x=7 and y=3

Case 2: if y=7

$$=$$> 26+x+7 = multiple of 9

$$=$$> 33+x = multiple of 9

$$=$$> The possible value of x is 3

Since x>y, Case 2 is not possible

$$\therefore\ $$ x=7 and y=3

$$=$$> (2x+3y) = 2(7)+3(3) = 23

Hence, the correct answer is Option D