Average of 20 numbers is 65. If the average of the first eight and last six numbers is 75.5 and 55.5 respectively, and if the twelfth number is 25% more than the eleventh number and the thirteenth number is (40/9)% less than the twelfth number, then find the twelfth number.
ATQ, Let the eleventh number be 10x. So, the twelfth number = 1.25 × 10x = 12.5x. Thirteenth number = 850/9 × 1/100 × 12.5x = 17x/3. So, 10x + 12.5x + 17x/3 = 65 × 20 – 8 × 75.5 – 6 × 55.5 = 360. Or, 100x/3 = 360. Or, x = 10.8. So, the twelfth number = 12.5 × 10.8 = 135.
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