Question : According to Raghav, his weight is more than 64 kg but less than 74 kg. His sister does not agree with Raghav and she thinks that his weight is more than 60 kg but less than 69 kg. His mother's view is that his weight cannot be more than 68 kg. His father's view is that his weight cannot be more than 67 kg. If all are them are correct in their estimation, then what is the average of different probable weights of Raghav measured (in kg)?
Option 1: 66
Option 2: 67
Option 3: 68
Option 4: 65
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Correct Answer: 66
Solution :
Let $x$ be the weight of Raghav.
According to Raghav,
$64 < x < 74$ -----------(i)
According to his sister,
$60 < x < 69$ ---------(ii)
According to his father,
$x \leq 67$ --------(iii)
According to his mother,
$x \leq 68$ --------(iv)
Taking the intersection of all inequalities (i), (ii), (iii) and (iv), we get:
$64 < x \leq 67$
Probable weights are 65, 66, and 67
$\therefore$ Average weight = $\frac{65+66+67}{3} = 66$
Hence, the correct answer is 66.
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