In Arun's opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest 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 are them are correct in their estimation, what is the average of different probable weights of Arun?

Interpret the statements

• Arun: weight > 65 and < 72
• Brother: weight > 60 and < 70
• Mother: weight ≤ 68 (“cannot be greater than 68”)

Step 1: Intersect the ranges
Lower bounds: max(65, 60) ⇒ > 65Upper bounds: min(72, 70, 68) ⇒ ≤ 68So possible weights = (65, 68]

Step 2: Consider likely integer weights
Probable integer weights consistent with all three: 66, 67, 68

Step 3: Average of the probable weights
Average = (66 + 67 + 68) ÷ 3 = 201 ÷ 3 = 67 kg

Notes

• We used integer weights because bathroom/medical scales typically report in whole kilograms in many textbook problems.
• The strict inequality “greater than 65” excludes 65; the mother's “cannot be greater than 68” includes 68.

Final Answer
Average of probable weights = 67 kg.