Question

Find a three digit number whose consecutive digits form a G.P. If we subtract 792 from this number whose digits are written in reverse order. If we increase the middle digit of a given number by 2, then the digits form an A.P. Find numbers?

Answer 1

let the number are $a{r}^2,ar,a$

given $a{r}^2,ar+2,a$ are in AP

so $2(ar+2)=a{r}^2+a$

$a(r-1{)}^2=4$ .............1

and given $a{r}^2\times 100+ar\times 10+a-792=a\times 100+ar\times 10+a{r}^2$

$a(r^2-1)=8$ .......2

from equation 1 and 2

$a=1,r=3$

so number are = 9,3,1