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The average age of a class of 20 students increases by 1, when the ave

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Bunuel
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The average age of a class of 20 students increases by 1, when the ave [#permalink] New post   26 Jan 2021, 10:00
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The average age of a class of 20 students increases by 1, when the average of the entire class is calculated considering the teacher whose age is 33 years. Find the average age of the class. (Excluding the teacher)

(A) 11 years
(B) 12 years
(C) 15 years
(D) 18 years
(E) 19 years
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B
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Re: The average age of a class of 20 students increases by 1, when the ave [#permalink] New post   26 Jan 2021, 10:28
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\(20x+33=21(x+1)\)

\(x=12\)

B
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Re: The average age of a class of 20 students increases by 1, when the ave [#permalink] New post   26 Jan 2021, 22:47
T/20=Average .... Eq1

T+33/21=A+1....Eq2

Substituting T=20A from eq 1 in EQ 2

20A+33/21=A+1
20A+33=21A+21
A=12
Answer option B 12

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Re: The average age of a class of 20 students increases by 1, when the ave [#permalink] New post   31 Jan 2021, 06:02
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Solution



Given
In this question, we are given that
    • The average age of a class of 20 students and 1 teacher = (average age of the 20 students) + 1
    • The age of the teacher = 33

To find
We need to determine
    • The average age of the 20 students

Approach and Working out
    • Let the average age of the 20 students be x
      o Then, the sum of the ages of these 20 students = 20x
      o Thus, the sum of the ages of these 20 students + age of the teacher = 20x + 33
         Hence, average age of the 20 students and 1 teacher = (20x + 33)/21

    • Now, since average age of a class of 20 students and 1 teacher = (average age of the 20 students) + 1, we get that:
      o (20x + 33)/21 = x + 1
      o 20x + 33 = 21x + 21
      o 33 – 21 = 21x – 20x
      o 12 = x

Thus, option B is the correct answer.

Correct Answer: Option B
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Re: The average age of a class of 20 students increases by 1, when the ave [#permalink]
31 Jan 2021, 06:02
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