Question

If the average of six consecutive even numbers is 25, the difference between the largest and smallest

number is:-

(1) 8 (2) 10 (3) 12 (4) 14​

Answer 1

☯︎ Aɴsᴡᴇʀ

• let the smallest number be x

then according to the question

( consecutive even numbers)

other numbers are;

• x + 2
• x + 4
• x + 6
• x + 8
• x + 10

__________________________

and it is given that sum average of these numbers is 25

$\boxed{ \bold{average \: = \frac{sum \: of \: numbers}{total \: no. \: of \: numbers} }}$

$\bold{: \implies25 = \frac{x + x + 2 + x + 4 + x + 6 + x + 8 + x + 10}{6} }$

$\bold{ : \implies \frac{6x + 30}{6} = 25} \\ \\ \bold{: \implies \frac{ \cancel{6}(x + 5)}{ \cancel{6}} = 25 } \\ \\ \bold{: \implies x + 5 = 25} \: \: \: \: \: \: \: \\ \\ \bold{ : \implies x = 25 - 5 } \: \: \: \: \: \: \: \\ \\ \bold{: \implies \boxed{ \bold{ x = 20}}} \: \: \: \: \: \: \: \: \: \: \:$

so, smallest number is 20

and others numbers are:

• 20 + 2 = 22
• 20 + 4 = 24
• 20 + 6 = 26
• 20 + 8 = 28
• 20 + 10 = 30

so, largest number is 30

now, we have to find difference between largest and smallest number.

➪ 30 - 20 = 10

therefore, option (2) is correct