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10 Jan 2019, 08:00
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E
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Difficulty:
75%
(hard)
Question Stats:
60% (02:52) correct
40%
(02:32)
wrong
based on 146
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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. 8
B. 9
C. 10
D. 12
E. 15
cfc198
Solve it using the logical approach.
Avg Age of students : Avg age of students incl teacher = 8:9
Age of teacher : Avg age of students = 3:1 = 24 : 8 (to make it comparable to ratio above.)
Say if teacher's age is 24, the students avg age is 8 which becomes 9 when the teacher is added to the group. The increase of 1 is because of the excess 16 (24 - 8 = 16) that the teacher brought in to divide evenly among all students and herself. Since everyone got 1 (the avg increased by 1), there must have been total 16 people (15 students + 1 teacher).
Hence number of students must be 15.
Answer (E)
General Discussion
Updated on: 10 Jan 2019, 23:10
Originally posted by Dare Devil on 10 Jan 2019, 18:55.
Last edited by Dare Devil on 10 Jan 2019, 23:10, edited 1 time in total.
Last edited by Dare Devil on 10 Jan 2019, 23:10, edited 1 time in total.
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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.
Let number of students in the class = x
Let the average age of the students = y
Let the age of the teacher = z
Given,
1) ratio of the average age of the class without the teacher to the average age including the teacher = 8 : 9
Average age of students and teacher = \((No.Of Students*Avg Age + Age of teacher)/(No.of students + 1)\)
= \((x*y + z)/(x+1)\)
Given this ratio = 8:9
\(y/((x*y + z)/(x+1)) = 8/9\)
\(y(x+1)/(x*y + z) = 8/9\)
\(xy + 9y = 8z\) -----------------------equation 1
2) Ratio of the teacher’s age and the average age of the students is 3 : 1
\(z/y = 3/1\)
\(z = 3y\) --------------------------------- equation 2
equation 2 in equation 1 implies,
\(xy + 9y = 8(3z)\)
\(xy = 15y\)
\(y(x-15) =0\)
Since y avg age can't be zero
\(x = 15\)
Number of students = 15
Option E is correct
Let number of students in the class = x
Let the average age of the students = y
Let the age of the teacher = z
Given,
1) ratio of the average age of the class without the teacher to the average age including the teacher = 8 : 9
Average age of students and teacher = \((No.Of Students*Avg Age + Age of teacher)/(No.of students + 1)\)
= \((x*y + z)/(x+1)\)
Given this ratio = 8:9
\(y/((x*y + z)/(x+1)) = 8/9\)
\(y(x+1)/(x*y + z) = 8/9\)
\(xy + 9y = 8z\) -----------------------equation 1
2) Ratio of the teacher’s age and the average age of the students is 3 : 1
\(z/y = 3/1\)
\(z = 3y\) --------------------------------- equation 2
equation 2 in equation 1 implies,
\(xy + 9y = 8(3z)\)
\(xy = 15y\)
\(y(x-15) =0\)
Since y avg age can't be zero
\(x = 15\)
Number of students = 15
Option E is correct
