Ram has many combinations of l and b for his value of area. Shyam's value of perimeter cannot be the same value that can be derived from the value of area that Ram knows. Hence, by hit and error method, eliminate the combinations that matches l and b from Ram's area and Shyam's perimeter. It can again be construed that by whatever Ram knows, two prime integers that produces the area value is not possible. Alternatively, the value of l and b cannot be the product of two prime numbers in A= l x b.Otherwise, it would have been possible for Ram to know the value of (l+b) and decode the value of parimeter in 2(l+b).Again, Shyam also knows that the sum of two prime integers cannot be used to find (l+b) though he knows the value of parimeter as a whole. Had it been true, Shyam would have known that Ram knows (l+b). The limitations are: l>b>1 P<=80 (l+b)<=40 The least possible combinations can be that of 2 and 3. But that is not possible since those two are prime numbers again. Hence lets start from integer 4 ( which is not prime): The values of (l+b) can be either 11, 17, 23, 27, 29 35 or37. Iteratively, break all these numbers by hit and trial of (l+b) and (lxb). You will come to 5x6 as the obvious answer.Also, Area = 30 and Perimeter = 22.