In Arun's opinion, his weight is greater than $6.5 k g$ but less than $72 k g$ $. H i s b r o t h e r d o e s t n o t a g r e e w i t h A r u n a n d h e t h i n k s A r u n s^{'} w e i g h t i s g r e a t e r t h a n$ 60\ kg $b u t l e s s t h a n$ 70\ kg $. H i s m o t h e r^{'} s v i e w i s t h a t h i s w e i g h t c a n n o t b e g r e a t e r t h a n$ 68\ kg$. If all are them are correct in their estimation, what is the average of different probable weights of Arun?

67 k g

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68 k g

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69 k g

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Data inadequate

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None of these

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Solution

The correct option is A $67 k g$ .
Let Arun's weight by X kg.
According to Arun, $65 < X < 72$
According to Arun's brother, $60 < X < 70$ .
According to Arun's mother, $X <= 68$
The values satisfying all the above conditions are $66, 67$ and $68$ .
$∴$ Required average $= (\frac{66 + 67 + 68}{3}) = (\frac{201}{3}) = 67 k g$ .

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The correct option is A 67 kg.Let Arun's weight by X kg.According to Arun, 65<X<72According to Arun's brother, 60<X<70.According to Arun's mother, X<=68The values satisfying all the above conditions are 66,67 and 68.∴ Required average =(66+67+683)=(2013)=67 kg.