Order and Ranking

 Order and Ranking is a reasoning topic that deals with arranging persons or objects in a sequence (based on height, weight, marks, age, etc.) and determining their positions or ranks.

🎯 Key Concepts Covered

Concept	Explanation
Rank from Top/Bottom	Position of a person from either end
Total number of people	Find total using given top/bottom ranks
Number of people between	Count between two persons
Possible position in a group	Max/min possible ranks
Interchanging positions	Switch and analyse

🔧 Important Formulas & Tricks

✅ Formula 1: Total Number of Persons

If a person is 5th from top and 6th from bottom:

Total = (Top Rank) + (Bottom Rank) – 1
Total = 5 + 6 – 1 = 10

✅ Formula 2: Number of Persons Between Two People

If A is 3rd from top and B is 6th from bottom in a line of 10:

No. between = Total – (Top Rank of A + Bottom Rank of B) + 1
             = 10 – (3 + 6) + 1 = 2

✅ Formula 3: When Positions are Interchanged

If A is 6th from left, B is 8th from right, and they interchange positions in a row of 15:

New position of A from right = 15 – 6 + 1 = 10
New position of B from left = 15 – 8 + 1 = 8

🧩 Solved Examples with Diagrams

🔹 Example 1: Total Persons

Q: A is 5th from top and 6th from bottom. Find total number of persons.

✅ Solution:

Total = 5 + 6 – 1 = 10

Answer: 10 persons

Diagram:

Top ↓           ↑ Bottom
1 2 3 4 [A] 6 7 8 9 10

🔹 Example 2: Between Two Ranks

Q: Ravi is 10th from left, Sita is 9th from right in a line of 20. How many persons are between them?

✅ Solution:

No. between = 20 – (10 + 9) + 1 = 2

Answer: 2 persons

Diagram:

Left →  ...[Ravi]__2__ [Sita] ← Right

🔹 Example 3: Position After Interchange

Q: A is 5th from left, B is 7th from right in a row of 15. If they interchange positions, what is A’s new position from the right?

✅ Solution:
A’s new position = 15 – 5 + 1 = 11

Answer: 11th from right

🔹 Example 4: Min/Max Possible Rank

Q: In a race, Ram is 12th from top and Shyam is 15th from bottom. How many people could be in the race?

✅ Min. total = 12 + 15 – 1 = 26
✅ Max. total = Cannot be determined without overlap information

📊 Table Summary of Common Questions

Type of Question	Formula / Method
Total Persons (Top + Bottom – 1)	T = R₁ + R₂ – 1
Between Two Persons	T – (R₁ + R₂) + 1
Interchange Positions	New Rank = N – Old Rank + 1
From opposite end	Total – Given Rank + 1

📝 Quick Practice Challenge

Q: In a class of 50 students, Rani ranks 17th from the top. What is her rank from the bottom?

✅ Solution:

Rank from bottom = Total – Top Rank + 1 = 50 – 17 + 1 = 34

✅ Answer: 34th from bottom

🧠 Tips for Accuracy

• Use number lines or boxes to visualize.

• Double-check directions (top/bottom, left/right).

• Subtract 1 only when ranks overlap (same person).

• Practice with timing for exams.

🏁 Quick Recap Diagrams

🔄 Person’s Position in Line:

Top ↓        ↑ Bottom
1 2 3 4 5 6 ... n

↔ Between Two People:

[A] ---- x people ---- [B]

🧠 Practice Questions - Order & Ranking 

✅ Q1. In a row of 20 students, Ravi is 5th from the left. What is his position from the right?

Solution:
Position from right = Total – Left Rank + 1 = 20 – 5 + 1 = 16

Answer: 16th from right

Diagram:

Left → 1 2 3 4 [5-Ravi] ... 20 ← Right
                      ↑
                   16th from Right

✅ Q2. In a line of 30 students, Sita is 12th from the left and 17th from the right. How many students are there?

Solution:
Total = Left Rank + Right Rank – 1 = 12 + 17 – 1 = 28

Answer: 28 students

✅ Q3. A is 6th from the top and B is 9th from the bottom in a class of 20. How many students are between A and B?

Solution:
Between = Total – (Top Rank + Bottom Rank) + 1
= 20 – (6 + 9) + 1 = 6

Answer: 6 students

Diagram:

Top ↓
1 2 3 4 5 [6-A] _ _ _ _ _ _ [12-B] ... 20 ↑ Bottom

✅ Q4. In a row, Ankit is 10th from the left and Amit is 15th from the right. If there are 30 students, how many are between them?

Solution:
Between = Total – (10 + 15) + 1 = 30 – 25 + 1 = 6

Answer: 6 students

✅ Q5. Ram is 15th from left in a row of 40. What is his position from the right?

Solution:
= 40 – 15 + 1 = 26

Answer: 26th from right

✅ Q6. In a class of 50 students, Anu ranks 14th from the top. What is her rank from the bottom?

Solution:
= 50 – 14 + 1 = 37

Answer: 37th from bottom

✅ Q7. A student ranks 9th from the top and 28th from the bottom in an exam. How many students are there?

Solution:
= 9 + 28 – 1 = 36

Answer: 36 students

✅ Q8. In a line, Rani is 7th from the left and Meena is 10th from the right. If they interchange positions, Rani becomes 12th from the left. What is the total number of girls?

Solution:

After swap:
Rani → 12th from left
So Meena = 7th from left before

Now total = Rani's left position + Meena's right position – 1
= 12 + 10 – 1 = 21

Answer: 21 girls

✅ Q9. In a row, A is 18th from the left and B is 22nd from the right. If there are 40 students, how many students are between A and B?

Solution:

Total – (Left + Right) + 1 = 40 – (18 + 22) + 1 = 40 – 40 + 1 = 1

Answer: 1 student

✅ Q10. In a class, Tina ranks 8th from top and 27th from bottom. One student failed to attend. What is the total strength?

Solution:
Total = 8 + 27 – 1 = 34
+1 absent = 35

Answer: 35 students