Solution:Let the three digit number
X = pqr
X = (100 × p) + q(10) + r
= 100p + 10q + r ______(i)
All possible Value of ‘Y’ after permuting the digits
Y = prq, qpr, qrp, rpq, rqp
We consider first ‘prq’
Y = prq = 100p + 10r + q _____(ii)
eqⁿ(i) – eqⁿ(ii)
X – Y = (100p + 10q + r) – (100p + 10r + q)
= 9q – 9r = 9 (q – r)
∴ ‘X – Y’ will be divisible by ‘9’
Similarly for number y= qpr, qrp, rpq, rqp, the term (X – Y), will always divisible by ‘9’.