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.
.

(In reply to Without solving for M and N by K Sengupta)

I have found a shorter solution compared to my previous post and, this is as follows:

We have, N/(N+1) = 1/5 ..... (i)
M/(M+1) = M/5 .....(ii)

Dividing (ii) by (i), we have:

M(N+1)/N(M+1) = M
-> (N+1)/N(M+1) = 1
-> N+1 = N(M+1)
-> N+1 = M*N + N
-> M*N = 1 QED

Edited on January 11, 2012, 1:29 am

Posted by K Sengupta on 2012-01-11 01:25:31