Ther are 5 consecutive even numbers X1, X2, X3, X4, X5 and 4 consecutive odd numbers Y1, Y2, Y3, Y4.The average of the even numbers is 5 more than the average of the odd numbers. If the sum of the even numbers is 30 more than the sum of the odd numbers, find the average of the odd numbers.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 5.
Let the 4 consecutive odd numbers be:
Y1 = y − 3
Y2 = y − 1
Y3 = y + 1
Y4 = y + 3
Average of odd numbers = y
Sum of odd numbers = 4y
Let the 5 consecutive even numbers be:
X1 = e − 4
X2 = e − 2
X3 = e
X4 = e + 2
X5 = e + 4
Average of even numbers = e
Sum of even numbers = 5e
The average of even numbers is 5 more than that of odd numbers
⇒ e = y + 5
Also given:
The sum of even numbers is 30 more than the sum of odd numbers
⇒ 5e = 4y + 30
Substitute e = y + 5
⇒ 5(y + 5) = 4y + 30
⇒ 5y + 25 = 4y + 30
⇒ y = 5
Average of the odd numbers = 5