If you moved the 3 at the end of a certain large number to the beginning, it would be the same as multiplying it by 3. What is the number?

(In reply to answer by K Sengupta)

Assume that the number is of the form pqr.....3pqr.....3......pqr3

Let u = 0.pqr.....3pqr.....3......pqr3
Or,3.pqr.....3pqr.....3......pqr3 = u+3
or, 0.3pqr.....3pqr.....3pqr......3pqr = (u+3)/10

By the given conditions, we must have:

(u+3)/10 = 3*u
or, 30*u = u+3
or, u = 3/29
 =0.1034482758620689655172413793...........0.1034482758620689655172413793

Hence the number having the given property is 103,448,275,862,0689,655,172,413,793
 

 

Edited on March 21, 2008, 1:00 pm

Posted by K Sengupta on 2008-03-21 12:59:35