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Rank Difference Between Two Persons

Introduction

Many reasoning tests ask how many people stand between two given ranks. This pattern is quick to solve once you recognise the simple relationship between two ranks.

Mastering this helps in arrangement, ranking and ordering problems where you must count positions or gaps.

Pattern: Rank Difference Between Two Persons

Pattern

The key idea: Number of people between two ranks = |Rank₁ - Rank₂| - 1.

If ranks are given from the same end (top/left or bottom/right) use the absolute difference minus one. If ranks are from opposite ends, convert one rank to the same reference before applying the formula.

Step-by-Step Example

Question

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

Solution

  1. Step 1: Identify the two ranks

    A = 6th from top, B = 9th from top.

  2. Step 2: Compute the absolute difference

    |9 - 6| = 3.

  3. Step 3: Subtract 1 to get people in between

    Number between = 3 - 1 = 2.

  4. Final Answer:

    2 persons

  5. Quick Check:

    Ranks list (top → bottom): 1 ... 5, A(6), 7, 8, B(9), ... → two persons (7 & 8) between ✅

Quick Variations

1. If ranks are from opposite ends, convert one rank:

Left-to-right conversion: Left position L → Right position = Total - L + 1.

2. If asked "how many persons are not between them" use complementary counting (Total - persons between - 2).

3. If one rank equals the other, there are 0 persons between (same position).

Trick to Always Use

  • Step 1 → Ensure both ranks use the same reference (top/left or bottom/right).
  • Step 2 → Compute |Rank₁ - Rank₂| - 1 to get the number between.

Summary

Summary

  • Use |Rank₁ - Rank₂| - 1 to quickly find people between two ranks.
  • Convert ranks to the same end first if they are given from opposite ends.
  • Check edge cases: adjacent ranks → 0 between; same rank → 0 between.
  • For complementary questions (e.g., how many not between), use Total - between - 2.

Example to remember:
If A = 3rd and B = 7th (same reference) → between = |7 - 3| - 1 = 3 persons (4th, 5th, 6th).

Practice

(1/5)
1. In a row, Riya is 4th from the left and Neha is 9th from the left. How many people are sitting between them?
easy
A. 4
B. 3
C. 5
D. 6

Solution

  1. Step 1: Identify both ranks

    Riya = 4th, Neha = 9th from the same end.

  2. Step 2: Apply the formula

    Number between = |9 - 4| - 1 = 5 - 1 = 4.

  3. Final Answer:

    4 persons → Option A

  4. Quick Check:

    Positions 5, 6, 7, 8 lie between them → 4 ✅
Hint: Use |Rank₁ - Rank₂| - 1 when both ranks are from the same end.
Common Mistakes: Forgetting to subtract 1 after finding the difference.
2. Amit is 7th from the left and Sumit is 11th from the left. How many people are between them?
easy
A. 3
B. 2
C. 4
D. 5

Solution

  1. Step 1: Identify the two positions

    Amit = 7th, Sumit = 11th from the same side.

  2. Step 2: Apply the formula

    Number between = |11 - 7| - 1 = 4 - 1 = 3.

  3. Final Answer:

    3 persons → Option A

  4. Quick Check:

    8th, 9th, 10th are between → 3 ✅
Hint: Subtract smaller rank from larger and then subtract 1.
Common Mistakes: Using only the difference without subtracting 1.
3. In a line of students, A is 10th from the left and B is 15th from the left. How many students are between them?
easy
A. 3
B. 4
C. 5
D. 6

Solution

  1. Step 1: Note the given ranks

    A = 10th, B = 15th.

  2. Step 2: Apply formula

    Number between = |15 - 10| - 1 = 5 - 1 = 4.

  3. Final Answer:

    4 students → Option B

  4. Quick Check:

    11th, 12th, 13th, 14th are between → 4 ✅
Hint: Take difference of ranks and subtract 1.
Common Mistakes: Adding instead of subtracting ranks.
4. In a row of people, Priya is 12th from the left and Sneha is 19th from the same end. Find how many people are between them.
medium
A. 5
B. 7
C. 6
D. 8

Solution

  1. Step 1: Write the ranks

    Priya = 12th, Sneha = 19th from the left.

  2. Step 2: Apply the formula

    Number between = |19 - 12| - 1 = 7 - 1 = 6.

  3. Final Answer:

    6 persons → Option C

  4. Quick Check:

    13th to 18th positions → 6 people ✅
Hint: Always subtract 1 from the difference between ranks.
Common Mistakes: Using difference directly as answer.
5. In a class, Ramesh is 8th from the top and Suresh is 15th from the top. How many students are between them?
medium
A. 5
B. 8
C. 7
D. 6

Solution

  1. Step 1: Identify both positions

    Ramesh = 8th, Suresh = 15th (same reference).

  2. Step 2: Apply formula

    Number between = |15 - 8| - 1 = 7 - 1 = 6.

  3. Final Answer:

    6 students → Option D

  4. Quick Check:

    Positions 9-14 = 6 students ✅
Hint: Difference minus one gives the number between.
Common Mistakes: Forgetting to take the absolute difference.

Mock Test

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