The consecutive digits of a three-digit number are in G.P. If the middle digit is increased by 2, then they form 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 the three-digit number be xyz. According to given condition, we have
${\mathrm{y}}^2=\mathrm{xz}$…………..(1)
$2(\mathrm{y}+2)=\mathrm{x}+\mathrm{z}$…..(2)
$100\mathrm{x}+10\mathrm{y}+\mathrm{z}-792=100\mathrm{z}+10\mathrm{y}+\mathrm{x}$
$\Rightarrow \mathrm{x}-\mathrm{z}=8$……(3)
Squaring (2) and (3), and subtracting, we have
$4\mathrm{xz}=4(\mathrm{y}+2{)}^2-64$……….(4)
$\Rightarrow {\mathrm{y}}^2=(\mathrm{y}+2{)}^2-16 [\mathrm{Using}(1)]$
$\Rightarrow \mathrm{y}=3$
$\Rightarrow \mathrm{x}+\mathrm{z}=10 [\mathrm{Using}(2)]$
$\Rightarrow \mathrm{x}=9,\mathrm{z}=1$
Hence, the number is 931 =7² x 19.