Ranking and Order — Position from Top, Bottom, Left and Right

Ranking questions place people in a row or a list and ask for positions or the total number. One formula solves most of them.

1. Position from both ends

Total = position from left + position from right − 1

(We subtract 1 because the person is counted from both sides.)

The same works for top and bottom of a class.

Example 1

Riya is 12th from the top and 18th from the bottom of her class. How many students are in the class?

12 + 18 − 1 = 29.

Example 2

In a row of 40 students, Aman is 15th from the left. What is his position from the right?

From right = 40 − 15 + 1 = 26th.

2. People between two persons

Example 3

In a row of 30, A is 8th from the left and B is 10th from the right. How many people are between them?

B from the left = 30 − 10 + 1 = 21. Between 8th and 21st: 21 − 8 − 1 = 12.

Example 4 — overlapping

In a row of 20, P is 14th from the left and Q is 12th from the right. How many are between them?

Q from the left = 20 − 12 + 1 = 9. Now Q (9th) is to the left of P (14th). Between = 14 − 9 − 1 = 4.

Always convert both positions to the same end before comparing.

3. Swapping positions

Example 5

In a row, A is 10th from the left and B is 15th from the right. They swap places; now A is 18th from the left. How many people are in the row?

After the swap, A sits in B's old seat. That seat is 18th from the left and 15th from the right → total = 18 + 15 − 1 = 32.

4. Comparison (who is tallest?)

Write the people in a line using > signs.

Example 6

A is taller than B but shorter than C. D is taller than C. Who is the tallest?

B < A < C < D → D is the tallest; B is the shortest.

Example 7

Among five friends, Kiran scored more than only Leela. Mohan scored less than Nitin but more than Kiran. Om scored more than Nitin. Who scored the most?

Leela < Kiran (Kiran beats only Leela) → Kiran < Mohan < Nitin < Om → Om.

Common mistakes

• Forgetting the "− 1" in the total formula.
• Comparing a "from left" position with a "from right" position directly.
• After a swap, using the person's old position instead of the seat's position.

Quick recap

• Total = left + right − 1.
• From right = total − from left + 1.
• Between = difference of positions (same end) − 1.
• Comparisons: write a chain with < signs.