Average of 22 numbers is 58. If the average of the first eight and last seven numbers is 65.5 and 48.5 respectively, and if the eleventh number is 35% more than the tenth number and the twelfth number is (50/9)% less than the eleventh number, then find the eleventh number.
ATQ, Let the tenth number be 10x. So, the eleventh number = 1.35 × 10x = 13.5x. Twelfth number = 850/9 × 1/100 × 13.5x = 34x/3. So, 10x + 13.5x + 34x/3 = 58 × 22 – 8 × 65.5 – 7 × 48.5 = 290. Or, 100x/3 = 290. Or, x = 8.7. So, the eleventh number = 13.5 × 8.7 = 117.45.
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