# If n is a positive integer such that n/810=0.d25d25.......where d is a single digit in decimal base.Find n.

Chetan Mandayam Nayakar
312 Points
9 years ago

USE THE FACT THAT

0.d25d25...=d25(10^(-3) +10^(-6)+...)

=d25(10-3/(1-10-3)) by INFINITE GEOMETRIC PROGRESSION

Asan Kumar
31 Points
9 years ago

n= 750

swarali viraj
16 Points
9 years ago

Could you please explain it ?

swarali viraj
16 Points
9 years ago

Can you please explain Mr.Asan Kumar as how you got 75?

Aaryendra Chhabra
24 Points
5 years ago
n/810=0.d25d25....       equation 1
multiply both sides by 1000.
therefore, 1000n/810=d25.d25d25d25......       equation 2
equation 2 – equation 1
999n/810=d25
111n/90=d25
n=(d25 x 90)/111
n=(d25 x 30)/37
as written in the question that ‘n’ is a positive integer.
therefore,d25 must be a multiple of 37.
and also ‘d’ is single digit.
therefore, by putting value of ‘d’ from 0 to 9 we get that by putting value of ‘d’ =9.
the condition is satisfied.
therefore, n= (925 x 30)/37
n= 25 x 30
n= 750