Question
The average of 16 numbers is 75. The first six numbers
and the last five numbers have averages of 90 and 72 respectively. The ninth number exceeds the eighth number by 20%, and the tenth number is reduced by (50/9)% from the ninth number. Determine the value of the ninth number.Solution
Let eighth number is 10x
So, ninth number = 1.20 × 10x = 12x
Tenth number = 850/9 × 1/100 × 12x = 34x/3
So, 10x + 12x + 34x/3 = 75 × 16 – 6 × 90 – 5 × 72
= 1200 – 540 – 360
= 300
Or, 100x/3 = 300
Or, x = 9
So, ninth number = 12 × 9 = 108
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