Question
The average of 15 numbers is 84. The first seven numbers
and the last five numbers have averages of 92.5 and 72.5, 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 = 84 × 15 – 7 × 92.5 – 5 × 72.5 = 250 Or, 100x/3 = 250 Or, x = 7.5 So, ninth number = 12 × 7.5 = 90
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