Question : If the average of three consecutive even numbers is 20, then find the numbers.
Correct Answer 18, 20, and 22
Solution & Explanation
Solution
Shortcut Trick to find the numbers if the average of three consecutive numbers are given
Here, given
The average of three consecutive even numbers = 20
This means the number lies in the middle of the given three consecutive numbers will be the average
Therefore, number lies in middle of the given three consecutive even numbers = 20
Therefore, the first even number among the given three consecutive even numbers
= Number in the middle – 2
= 20 – 2 = 18
And, last even number among the given three consecutive numbers
= Number in the middle + 2
= 20 + 2 = 22
Thus, numbers are 18, 20, and 22 Answer
Procedure to find the numbers if the average of three consecutive even numbers are given
It is necessary to know the procedure, as it applies to solving all similar types of given problems, as shortcut tricks are not applicable everywhere.
Given, the average of three consecutive even numbers = 16
Thus, the smallest and the greatest number among the given three even numbers = ?
Let first even number = a
Therefore, the second consecutive even number = a + 2
And, the third consecutive even number = a + 4
Now,
Formula to find the
Average = Sum of observations/Numbers of observations
Therefore, the average of the given three consecutive even numbers
= Sum of the three consecutive even numbers/3
⇒ 20 = a+(a+2)+(a+4)/3
⇒ 20 = a+a+2+a+4/3
⇒ 20 = 3a + 6/3
After taking 3 as common from the numerator
⇒ 20 = 3 (a + 2)/ 3
⇒ 20 = a + 2
⇒ a + 2 = 20
After transposing 2 to RHS
⇒ a = 20 – 2
⇒ a = 18
Thus, first even number = 18
And, the second consecutive even number = a + 2
= 18 + 2 = 20
And, the 3rd and even number = a + 4
= 18 + 4 = 22
Therefore, the given consecutive three even numbers = 18, 20 and 22 Answer
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