A certain number N divided by one more than itself yields one fifth.

Another number M divided by one more than itself yields one fifth of itself.

It is quite easy to find the product M*N.

**Try to do it " by heart" i.e. no calc, no pen, no paper.**

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Not very sure whether this qualifies as a "by heart" solution, but here goes:

We have:

N/(N+1) = 1/5 ..... (i)

M/(M+1) = M/5 .....(ii)

From (ii), we have: M+1=5

Substituting this in both sides of (i):

(M*N + N)/(N+1) = (1/5)*5

-> M*N+N = N+1

-> M*N = 1 QED

*Edited on ***January 10, 2012, 4:01 am**