In Varun's opinion, his weight is greater than 65 kg but less than 72 kg. His father does not agree with Varun, and he thinks that Varun's weight is greater than 60 kg but less than 70 kg. His sister's view is that his weight cannot be greater than 68 kg. If all are correct in their estimation, what is the average of the different possible weights of Varun?

67

The following statement deduces the conclusion as follows:

Varun's opinion: 66, 67, 68, 69, 70, 71

Varun's father's opinion: 61, 62, 63, 64, 65, 66, 67, 68, 69, 70

Varun's sister's opinion: cannot be greater than 68 i.e., 66, 67, 68 (as according to Varun's opinion weight is greater than 65)

Thus, the possible combinations are 66, 67 and 68

Average = \(\frac{\text{66 + 67 + 68} }{3 }\)

Average = \(\frac{\text{201} }{3 }\)

Average = 67