Ranking and Order Notes & Questions | Class 5 Reasoning | Drishti OS

Ranking and Order

How to convert a rank from the top into a rank from the bottom, and back, using the total number of students.
How to find the total number of students when you know one person's rank from both ends.
How to work out one person's rank when you know another person's rank and the gap between them.

Formula: Rank from bottom = Total students - Rank from top + 1

Example: 30 students, rank 5th from top -> rank from bottom = 30 - 5 + 1 = 26th.

Formula: Total students = Rank from top + Rank from bottom - 1

Example: Rank 6th from top and 10th from bottom -> total = 6 + 10 - 1 = 15 students.

Verbal: If you know how many places apart two people are, you can find one person's rank once you know the other's.

In a class of 25, Kabir ranks 4th from the top. What is his rank from the bottom?

Step 1 - Formula: rank from bottom = total - rank from top + 1
Step 2 - = 25 - 4 + 1
Answer: 22nd

Priya ranks 7th from the top and 9th from the bottom. How many students are there?

Step 1 - Formula: total = rank from top + rank from bottom - 1
Step 2 - = 7 + 9 - 1
Answer: 15

Mistake	Why it happens	Fix
Forgetting to add/subtract 1	Confusing rank with a plain count	Always apply the '+1' or '-1' in the formula
Mixing up top and bottom	Not reading the question carefully	Underline which rank ('top' or 'bottom') is given
Wrong gap direction	Assuming the second person ranks better	Check if the person is 'below' (worse rank) or 'above' (better rank)
Adding instead of using the formula	Trying to guess	Write the formula down before substituting numbers

In a class of 40, a student ranks 10th from the top. What is the rank from the bottom?
A student ranks 5th from top and 8th from bottom. How many students are there in total?
If Aman is 3 ranks below Bela, and Bela is 6th from the top, what is Aman's rank from the top?
Stretch: In a class of 32, a student is exactly in the middle rank from both top and bottom. What is that rank?

Revision tip: Write the two formulas on a sticky note until they become automatic.

Open the Practice tab for graded questions on Ranking and Order.