cfc198 wrote:

The ratio of the average age of the class without the teacher to the average age including the teacher is 8 : 9. If the ratio of the teacher’s age and the average age of the students is 3 : 1, find the number of students.

A. 8

B. 9

C. 10

D. 12

E. 15

(A)

A logical way..(I) If s students are there, the strength with the addition of a teacher becomes s+1..

(II) However, teacher's age is 3 times the average of students average age, we can take instead of teacher we are adding the 3 students to total students, say s... so s+3

Therefore, final ratio 8:9 will be similar to ratio s=1 : s+3..

\(\frac{8}{9}=\frac{s+1}{s+3}.....9(s+1)=8(s+3)......9s+9=8s+24......s=24-9=15\)

(B)

If you do not understand the reasoning behind the above solution..# of students = s and average age = a... so total age = as

# after addition of teacher = s+1, and age of teacher = 3a...so total age = as+3a... average age now = \(\frac{as+3a}{s+1}=\frac{a(s+3)}{s+1}\)

Thus initial average age : average age after addition = a : \(\frac{a(s+3)}{s+1}\) = 8:9.....1 : \(\frac{(s+3)}{s+1}\) = 8:9..

\(9*1=\frac{(s+3)}{s+1}*8....9(s+1)=8(s+3)......9s+9=8s+24......s=24-9=15.\)

E

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372

2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor