10 Consecutive numbers are given. If the average of the two numbers given in the middle is 13.5, then what is the sum of the first 6 numbers?

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SSC CHSL Tier-I Exam 2022 Official Paper (Held On: 16 March, 2023 Shift 2)
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  1. 58
  2. 55
  3. 67
  4. 69

Answer (Detailed Solution Below)

Option 4 : 69
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Detailed Solution

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Given

10 consecutive numbers.

Average of the middle two numbers = 13.5.

Concept:

We'll use the property that the average of two middle numbers in a series of consecutive numbers is the average of the whole series.

Solution:

The average of the whole series of 10 numbers is also 13.5.

Hence, the first number = 13.5 - 4.5 = 9 (since the average is the middle of the series of 10 numbers).

Sum of first 6 numbers = 6 × average of first and sixth number = 6 × (9+14)/2 = 69.

Therefore, the sum of the first 6 numbers is 69.

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