Question
The average of 18 numbers is 70. The first eight
numbers have an average of 90, and the last five numbers have an average of 48. The eleventh number exceeds the tenth number by 20%, and the twelfth number is reduced by (50/9)% from the eleventh number. Determine the value of the eleventh number.Solution
Let tenth number is 10x
So, eleventh number = 1.20 × 10x = 12x
Twelfth number = 850/9 × 1/100 × 12x = 34x/3
So, 10x + 12x + 34x/3
= 70 × 18 – 8 × 90 – 5 × 48
= 1260 – 720 – 240
= 300
Or, 100x/3 = 300
Or, x = 9
So, eleventh number = 12 × 9 = 108
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