Question
The average of 19 numbers is 80. The first eight numbers have an average of 100, and the last six numbers have an average of 70. The twelfth number exceeds the eleventh number by 20%, and the thirteenth number is reduced by (50/9)% from the twelfth number. Determine the value of the twelfth number.
Solution
Let eleventh number is 10x
So, twelfth number = 1.20 × 10x = 12x
Thirteenth number = 850/9 × 1/100 × 12x = 34x/3
So, 10x + 12x + 34x/3 = 80 × 19 – 8 × 100 – 6 × 70
= 1520 – 800 – 420
= 300
Or, 100x/3 = 300
Or, x = 9
So, twelfth number = 12 × 9 = 108
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