Question
The average of 17 numbers is 80. The first seven
numbers have an average of 100, and the last five numbers have an average of 72. The tenth number exceeds the ninth number by 20%, and the eleventh number is reduced by (50/9)% from the tenth number. Determine the value of the tenth number.Solution
Let ninth number is 10x
So, tenth number = 1.20 Ă— 10x = 12x
Eleventh number = 850/9 Ă— 1/100 Ă— 12x = 34x/3
So, 10x + 12x + 34x/3 = 80 × 17 – 7 × 100 – 5 × 72
= 1360 – 700 – 360
= 300
Or, 100x/3 = 300
Or, x = 9
So, tenth number = 12 Ă— 9 = 108
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