The average age of a class, including the teacher is 1.5 years more th

Question

The average age of a class, including the teacher is 1.5 years more than the average age of the class when the teacher is not considered. If the teacher is 30 years older than the average age of the students, find the number of students in the class.

(1) 27
(2) 24
(3) 20
(4) 19
(5) 18

(1) 27
(2) 24
(3) 20
(4) 19 
(5) 18

Ish1996 · Answer

anyone have a solution for this?

ScottTargetTestPrep · Answer

We can let n = the number of students and x = the average age of the students. So we have:

(30 + x + nx)/(n + 1) = x + 1.5

30 + x + nx = (x + 1.5)(n + 1)

30 + x + nx = nx + x + 1.5n + 1.5

30 = 1.5n + 1.5

1.5n = 28.5

n = 19

Answer: D/4

Kunal112 · Answer

Sum of students age's = S No. of students = n Average = x Age of teacher = x + 30
S/n = x (Statement 1)

Also, (S + x + 30)/(n + 1) = x + 1.5 (It is given that average with teacher is 1.5 more than regular average)

(nx + x + 30) = (n + 1)(x + 1.5) here we substituted S = nx from statement 1
Solving this we will get

n = 19

Option D is correct

asfandabid · Answer

According to the question, the teachers age is 30 more than the average age of all students. Thus including the age of the teacher increases the average age by 1.5 years. Divide 30 by 1.5 to get 20 as the total number of people in class including the teacher. Hence the number of students is 19.

Kinshook · Answer

Let n be number of students and let x be average age of a student excluding teacher.

x n + x + 30 = (n+1) (x + 1.5) 
x (n+1) + 30 = x (n+1) + 1.5 (n+1) 
n+1 = 30/1.5 = 20
n = 19

IMO D

Kinshook · Answer

Please change the answer choices as below:-

(A) 27
(B) 24
(C) 20
(D) 19 
(E) 18

Abhishek009 · Answer

So, 30/1.5 = 20 is the total members including the teacher.

So, The number of members in the class excluding the teacher is 20-1 = 19 , Answer must be (4)

Shishou · Answer

the teachers age is divided such that the average age,including the teacher's increases by 1.5 . So we get 30/1.5=20 so 20 people had 1.5 added to their average age.
This includes the teacher so we will take him out and get 19.

answer is D

adewale223 · Answer

Let y be sum of students age

and n be number of students

Let teacher's age be x

y+x/n+1 - y/n = 1.5

Second statement

x = y/n + 30

xn = y +30n

From the first equation.

y + x - y(n+1)/n = 1.5(n+1)

yn + xn - y(n+1) = 1.5n(n+1)

Sub for xn

ny + y + 30n -yn - y = 1.5n^2 + 1.5n

30n - 1.5n = 1.5n^2

28.5 = 1.5n

n = 19

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The average age of a class, including the teacher is 1.5 years more th

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