The average of 10 consecutive even numbers is 25. If two even number just preceding the smallest of the 10 given numbers is also included, then what will be the new average?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3i.e 23
Concept Used :
Sum of terms = Average × Number of terms
Given that, average of 10 consecutive even numbers is 25.
Sum of 10 numbers = 25 × 10 = 250.
Now, let the 10 consecutive numbers be x, (x+2), (x + 4), (x + 6), (x + 8), (x + 10), (x + 12), (x + 14), (x + 16), (x + 18).
Sum of 10 terms = x + (x+2) + (x + 4) + (x + 6) + (x + 8) + (x + 10) + (x + 12) + (x + 14) + (x + 16) + (x + 18)
⇒ 250 = 10x + 90
⇒ 10x = 250 -90
⇒ 10x = 160
⇒ x = 160/10
⇒ x = 16.
Now, thw two even numbers preceding the smallest numbers are 14 and 12.
Now the new average = (250 + 26)/12
⇒ 276/12 = 23.
Hence the required average is 23.