The average of four consecutive odd natural numbers is eight less than the average of three consecutive even natural numbers. If the sum of these three even numbers is equal to the sum of the above four odd numbers, then the average of four original odd numbers is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 24.
| Understanding/Application |
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Let the consecutive odd natural numbers are a, a + 2, a + 4, a + 6. Let the three consecutive even natural numbers be b, b + 2, b + 4. Average of 4 consecutive odd natural numbers = (a + a + 2 + a + 4 + a + 6)/4 = a + 3 Average of 3 consecutive even natural numbers = (b + b + 2 + b + 4)/3 = b + 2 |
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a + 3 = b + 2 - 8 b - a = 9 .....(1 b + b + 2 + b + 4 = a + a + 2 + a + 4 + a + 6 3b = 4a + 6 3b - 4a = 6 ....(2 Solving 3(1) - (2), we get - (3b - 3a) - (3b - 4a) = 27 - 64 a = 21 Average of 4 consecutive odd natural number = a + 3 = 21 + 3 = 24 |