Position & Rank

• Find a person's position from the left or from the right in a line.
• Use the formula: position from other side = Total − position + 1.
• Find the total number of people from two given positions.

Level 1 — Core idea

Verbal: If there are 10 children in a line and Asha is 4th from the left, count backwards from the end to find her position from the right.

Symbolic: Position from right = Total − Position from left + 1. Total = Position from left + Position from right − 1.

Visual: Picture a line of children. Counting from the left gives one number; counting from the right for the same child gives a different number, but both describe the same spot.

Level 2 — Going deeper

These two formulas are really the same idea written two ways. If you know any two of "total", "position from left", and "position from right", you can always find the third.

NCERT anchor

NCERT Math Mela, Class 3 — Position and ordinal numbers (1st, 2nd, 3rd...) builds directly into this line-position reasoning.

In a line of 12 students, Rohan is 5th from the left. What is his position from the right?

Step 1 — Total = 12, Position from left = 5.
Step 2 — Position from right = 12 − 5 + 1 = 8.
Answer: 8th from the right

Meera is 3rd from the left and 6th from the right. How many students are in the line?

Step 1 — Total = Position from left + Position from right − 1.
Step 2 — Total = 3 + 6 − 1 = 8.
Answer: 8 students

• In a line of 15, Kabir is 6th from the left. Position from the right?
• In a line of 20, Diya is 9th from the right. Position from the left?
• Vihaan is 4th from the left and 5th from the right. Total students?
• Stretch: In a line of 30, Sara is 12th from the left. Position from the right?

Revision tip: Draw a short line with dots and count both ways to double-check.

Open the Practice tab for graded questions on Position & Rank.