Ramesh bought eight balls which were of the same weight, size and colour. He kept them in a bag. Harish, his younger brother, came home after some times and put his ball in the same bag. The balls Harish put in the bag was similar to the ones which Ramesh had put in, but its weight was different from Ramesh’s balls. When Harish came for the ball after sometime, he insisted on having his own ball.

Now Ramesh faced a problem. He had to find Harish’s ball from the whole lot. Suddenly an idea striked him that he should use a weighing machine. So, he procured one from his friend Suresh and started sorting Harish’s ball.

Can you help Ramesh in finding the ball that belonged to Harish in minimum time? Also state whether his ball was lighter or heavier than Ramesh’s balls?

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Answer:

To begin with, we shall divide the 9 balls in 3 heaps of 3 balls each. Suppose the heaps are ‘A’, ‘B’, ‘C’

First weighing

We will place heap ‘A’ on one pan of the balance and heap ‘B’ on the other. There are three possibilities:

(1) ‘A’= ‘B’ (2)’A’ heavier than ‘B’ (3) ‘B’ heavier than ‘A’

Second Weighing

Stage 1- Second weighing –‘A’ and ‘C’ to be put on pans. If ‘A’ is heavier than ‘C’, Then Rakesh‘s ball is lighter than that of Mukesh’s. And if ‘A’ is lighter than ‘C’, Rakesh’s ball is heavier. At this stage it will come out that Rakesh’s ball is in heap ‘C’.

Stage 2-‘A’ and ‘C’ will be put on pans. If ‘A’ and ‘C’ are equal then Mukesh’s ball is in heap ‘B’ and is heavier. If ‘C’ is heavier than ‘A’, Rakesh’s ball is lighter and is in heap ‘A’.

Stage 3- ‘B’ and ‘C’ will be put on pans. If ‘B’ and ‘C’ are equal then Rakesh’s ball is heavy and is in heap ‘A’. If ‘C’ is heavier than ‘B’, Then Rakesh’s ball is light and is in heap. Thus we would come to know the exact heap where Rakesh’s ball exist and whether it is heavy or light in weight in comparison with Mukesh’s ball.

Third weighing

In the third weighing experiment, we take any two balls from Rakesh’s heap. Now, if these two weight equal, the third ball belongs to Rakesh. If the scale in uneven, the raised pan has Rakesh’s ball because it (the ball) is lighter and its pan will lift up. In case the ball is heavy, it is in the lower pan of the balance. Weighing these balls three times we find out Rakesh’s ball and also known whether it is lighter or heavier than Mukesh’s.