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.

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Avg age of students : Avg age of students including teacher = 8:9

Age of teacher : Avg age of students = 3:1 = 24:8 (to make it comparable to the ratio above)

If teacher's age is 24, the students' average 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 be divided evenly among all students and herself.…

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What this question tests

What it tests

Your ability to convert between fractions, ratios, and decimals and to reason proportionally.

Common trap

Cross-multiplying incorrectly or mixing up the ratio parts — a part:part ratio is not a fraction of the whole.