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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?

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Solution

let the number are ar2,ar,a

given ar2,ar+2,a are in AP

so 2(ar+2)=ar2+a

a(r1)2=4 .............1

and given ar2×100+ar×10+a792=a×100+ar×10+ar2

a(r21)=8 .......2

from equation 1 and 2

a=1,r=3

so number are = 9,3,1

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