Building a Play House

         Rakesh and Nikhilesh were carrying pieces of timber to build a playhouse. Nikhilesh said to Rakesh ‘Give me one of your pieces so that we shall both be carrying the same number of pieces’.

          ‘No’ said Rakesh, proudly wanting to display his strength ‘give me one of yours and I shall be varying twice your weight.’

          Can you tell how many pieces of timber was each Rakesh and Nikhilesh carrying?

Answer:     Rakesh was carrying 5 pieces of lumber and Nikhilesh 7. Supposing Nikhilesh had n pieces. If he gave 1 piece to Rakesh, he would have n -1 piece.

                 But Rakesh would have then the same number as Nikhilesh. Therefore the total number of pieces must have been:

n-1 + n -1 or 2n – 2

Since Nikhilesh had n originally, Rakesh must have had 2n-2 - n or n-2.

If Rakesh gave Nikhilesh would have n + 1.

But we have the information that

N+1 is twice n -3

i.e.    n+ 1 = 2(n-3)

Or    n + 1 = 2n -6

Or       7 = n

5 = n-3