If average of $6$ consecutive numbers is $48$ , what is the difference between the smallest and the largest numbers ?

5

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10

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9

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data inadequate

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Solution

The correct option is B $5$
Let the $6$ numbers are $x, x + 1, x + 2, x + 3, x + 4, x + 5$ .
Since,
$a v e r a g e = 48$
$\frac{x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5}{6} = 48$
$6 x + 15 = 288$
$6 x = 273$
$x = 45.5$
So,
The smallest number $= 45.5$
The largest number $= x + 5 = 45.5 + 5 = 50.5$
Difference $= 50.5 - 45.5 = 5$

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