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A list contains nine numbers. The ratio of average of first five numbers, average of last five numbers and the average of all the numbers is 16 ∶ 14 ∶ 15. Upon adding 6 as the 10th number, there is no increase in average. What is the fifth number?

A list contains nine numbers. The ratio of average of first five numbers, average of last five numbers and the average of all the numbers is 16 ∶ 14 ∶ 15. Upon adding 6 as the 10th number, there is no increase in average. What is the fifth number? Correct Answer 6

Since adding number 6 does not change the average, ∴ Original average = 6

Average of first 5 numbers = 16/15 × 6 = 6.4

Sum of first 5 numbers = 5 × 6.4 = 32

Average of last 5 numbers = 14/15 × 6 = 5.6

Sum of last 5 numbers = 5 × 5.6 = 28

Sum of all numbers = 9 × 6 = 54

5th Term = Sum of first 5 numbers + Sum of last 5 numbers – Sum of 9 numbers

⇒ 32 + 28 – 54 = 6

∴ Fifth number is 6.

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