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Given a three digit number whose digit are the three successive terms of a G.P. If we subtract 792 from it,we get a number written by the same digit in reverse order.Now if we subtract four from the hundred's digit of the initial number and leave the other digit unchanged,we get a number whose digit are successive terms of an A.P. Find the number.

Given a three digit number whose digit are the three successive terms of a G.P. If we subtract 792 from it,we get a number written by the same digit in reverse order.Now if we subtract four from the hundred's digit of the initial number and leave the other digit unchanged,we get a number whose digit are successive terms of an A.P. Find the number.

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1 Answers

Arun
25750 Points
5 years ago
Let our number's digits be ar² ar a
So, we have our number as
ar²(100) + ar(10) + a
Now, if we subtract 792 from this, we get our digits reversed, so
ar²(100) + ar(10) + a - 792 = a(100) + ar(10) + ar²
100ar² + 10ar + a - 792 = 100a + 10ar + ar²
99ar² - 792 = 99a
ar² - 8 = a
a(r² - 1) = 8....(1)
 
now if we subtract 4 frm the hundred digit
 
ar² , ar – 4, a   are in A.P.
 
2ar – 8 = a(1+r²)
 
use this and the earier equation to find a and r.

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