Question

A three digit number whose consecutive digits form a G .P. If we subtract 792 from this number, we get a number consisting of the same digits written in the reverse order. Now if we increase the second digit of the required number by 2, the resulting number will form an A.P. Then the number is-

• A. $139$
• B. $927$
• C. $931$
• D. $763$

Answer 1

The correct option is C $931$

Let the three digit be $a$, $ar$, $a{r}^2$ then according to hypothesis
$100a+10ar+a{r}^2+792=100a{r}^2+10ar+a,i.e.a(r^2-1)=8$ and $a,ar+1,a{r}^2$ are in A.P.
then $2(ar+1)=a+a{r}^2$ so $r=3$ & $a=1$.
Thus digits are $1,3,9$ and so the required number is $931$