Question

In Arun’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother does not agree with Arun and he thinks that Arun’s weight is greater than 60 kg but less than 70 kg. His mother’s view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, then what is the average of the different probable weights of Arun?
(a) 67 Kg,
(b) 68 kg,
(c) 69 kg,
(d) Data Inadequate,
(e) None of these.

Answer 1

Hint: We start solving the problem by writing the interval for the weight of the Arun using the views of him, his brother and his mother. We then find the common interval for all the intervals that we have just found. We then find the probable weights using the common interval. We then find the average of the obtained probable weights using the definition of Mathematical Average.

Complete step by step answer:
According to the problem, we are given that Arun's weight is greater than 65 kg but less than 72 kg according to him and his brother does not agree with Arun and he thinks that Arun’s weight is greater than 60 kg but less than 70 kg. But Arun’s mother said that his weight cannot be greater than 68 kg. We need to find the average of different probable weights of Arun if all them are correct in their estimation.
We get the interval of probable weight of Arun according to his view as $65 < W < 72$, the interval of probable weight of Arun according to his brother’s view as $60 < W < 70$ and the interval of probable weight of Arun according to his brother’s view as $W \le 68$.
From the three intervals, we get the common interval for weights as $65 < W\le 68$.
So, we get the probable weights of Arun as 66 kg, 67 kg, 68 kg.
Let us take the average of 66 kg, 67 kg, 68 kg.
We know that the average of the terms a, b, c is $\dfrac{\left( a+b+c \right)}{3}$.
So, the average weight of weights 66 kg, 67 kg, 68 kg is $\dfrac{66+67+68}{3}=\dfrac{201}{3}=67kg$.

∴ The average of the probable weights of Arun is 67 kg.

Note: Here we have assumed that the weight is present in integers. We can also take the decimals for the probable weights of the Arun, but if we go on taking every decimal that will give us a total of infinity which will not be a suitable case for this problem. We should take the mathematical average for the obtained probable weights. We should not confuse the common interval of the weights.