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 is that 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, what is the average of different probable weights of Arun?

A. 67 kg B. 68 kg C. 69 kg D. Data inadequate Answer: Option A
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Solution(By Apex Team)

Let Arun’s weight be X kg. According to Arun, 65 < X < 72 According to Arun’s brother, 60 < X < 70 According to Arun’s mother, X ≯ 68 i.e. X ⩽ 68 The values satisfying all the above conditions are 66, 67 and 68 ∴ Required average $\begin{array}{l}=\left(\Large\frac{66+67+68}{3}\right)\mathrm{kg}\\ =\left(\Large\frac{201}{3}\right)\mathrm{kg}\\ =67\mathrm{~kg}\end{array}$

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