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      Question

      In a school there are 20 girls. The average age of the

      girls is decreased by 2 months when one girl aged 18 years is 8 replaced by a new girl. What is the age of the new girl?
      A 14 years 2 months Correct Answer Incorrect Answer
      B 14 years 4 months Correct Answer Incorrect Answer
      C 14 years 6 months Correct Answer Incorrect Answer
      D 14 years 8 months Correct Answer Incorrect Answer

      Solution

      Let the sum of age of 19 girls be x years and the Age of the new girls be y years. Old Average = (Sum of the age of 19 girls + Age of the girl to be replaced)/Total number of girls => (x + 18) / 20 New Average = (Sum of the age of 19 girls + Age of the new girl) / 20 According to the question, As we know The average age of the girls is decreased by 2 months when one girl aged 18 years is replaced i.e. Old Averag - New Average = 2 month ⇒ {(x + 18)/20} – {(x + y)/20} = (2/12) ⇒ 18 – y = 10/3 ⇒ y = 44/3 years ⇒ y = 14 years 8 months ∴ The age of new girl is 14 years 8 months.

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