The consecutive digits of a three digit number are in G.P. If the middle digit increased by 2, then they from an A.P. If 792 is subtracted from this, then we get the number constituting of same three digits but in reverse order. Then number is divisible by

Let three digits be xyz $\Rightarrow$ given y² = xz   ...(1)
$\Rightarrow$ 2(y + 2) = x + z    ...(2)
$\Rightarrow$ 100x + 10y + z – 792 =100z + 10y + x
$\Rightarrow$ x–z = 8      ...(3) (2)² - (3)² then
$\Rightarrow$ 4xz = 4(y + 2)² – 64    ...(4)
from (1) 

y² = (y + 2)²–16 $\Rightarrow$ y = 3 and x + z = 10
$\Rightarrow$ x = 9, z = 1 Now xyz = 931 = 7².19