In Arun’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother thinks that Arun’s weight is greater than 60 kg but less than 70 kg. His mother believes that h... In Arun’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother thinks that Arun’s weight is greater than 60 kg but less than 70 kg. His mother believes that his weight cannot be greater than 68 kg. If all are correct in their estimation, what is the average of different probable weights of Arun? Read more

Steps to Solve

1. Identify weight ranges
   Arun believes his weight is between 150 and 170 pounds. His brother thinks his weight is between 160 and 180 pounds, and his mother estimates it to be between 155 and 175 pounds. So we have:

   • Arun: $[150, 170]$
   • Brother: $[160, 180]$
   • Mother: $[155, 175]$

2. Determine the overlapping range
   Next, we find the overlapping range of all three estimates. The lower bound of the overlapping range is the highest of the three minimum weights, and the upper bound is the lowest of the three maximum weights. We calculate:

   • Lower bound: $\max(150, 160, 155) = 160$
   • Upper bound: $\min(170, 180, 175) = 170$

   Thus, the overlapping range is $[160, 170]$.

3. Calculate the average of the overlapping range
   The average weight in this range can be calculated using the formula for the average of two numbers: $$ \text{Average} = \frac{\text{Lower Bound} + \text{Upper Bound}}{2} $$ Plugging in the values: $$ \text{Average} = \frac{160 + 170}{2} = \frac{330}{2} = 165 $$