1.

The average of the three numbers x, y and z is 45. x is greater than the average of y and z by 9. The average of y and z is greater than y by 2. Then the difference of x and z is1). 32). 53). 74). 11

Answer»

ACCORDING to the question,
$ \RIGHTARROW \frac{{x + y + Z}}{3} = 45 $ $ \Rightarrow x + y + z = 135.....(i) $ $ \Rightarrow x = \frac{{y + z}}{2} + 9 $ $ \Rightarrow 2x - y - z = 18.....(ii) $ $ x + y + z = 135 $ $ \underline {2x - y - z = 18} $ $ 3x = 153 $ $ x = 51 $
From (i)
$y + z = 135 - 51 = 84.....(iii)$
Also,
$ \Rightarrow \frac{{y + z}}{2} = y + 2 $ $ \Rightarrow y + z = 2y + 4 $ $ \Rightarrow z - y = 4 $ $ + y + z = 84 $ $ \underline { - y + z = 4} $ $ \,\,\,\,\,\,\,\,\,2Z = 88 $ $ \,\,\,\,\,\,\,\,\,\,\,\,z = 44 $
Required difference
$= 51 - 44 = 7 $



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