Order Ranking
Key Concepts
| # | Concept | Explanation |
|---|---|---|
| 1 | Left-to-Right Rank | Position counted from the left end; smaller number = closer to left. |
| 2 | Right-to-Left Rank | Position counted from the right end; smaller number = closer to right. |
| 3 | Complementary Rank | Left rank + Right rank – 1 = Total persons. (Never forget the “–1”.) |
| 4 | Over-lap Count | When two ranks given for same person, use: Total = (R1 + R2) – 1. |
| 5 | Middle Person | For odd total, middle rank = (Total + 1)/2; for even, two middles. |
| 6 | Inter-change Shift | Swapping two persons shifts their old ranks; net change = 2 × distance between them. |
| 7 | Row-&-Column Matrix | Treat each row/column as independent line; apply rank formulas separately. |
| 8 | “Both sides” question | If A is r-th from left & s-th from right, total = r + s – 1. |
15 Practice MCQs
1. In a row of 40 boys, Ram is 15-th from left. What is his rank from right?
**Answer:** 26 **Solution:** Right rank = Total – Left rank + 1 = 40 – 15 + 1 = 26. **Shortcut:** 40 + 1 – 15 = 26. **Tag:** Complementary Rank2. Kavya is 9-th from left & 11-th from right in a row. How many girls?
**Answer:** 19 **Solution:** Total = 9 + 11 – 1 = 19. **Shortcut:** Add ranks, subtract 1. **Tag:** Over-lap Count3. In a queue of 50, Mohan is 20-th from front. What is his position from back?
**Answer:** 31 **Solution:** 50 – 20 + 1 = 31. **Tag:** Left-to-Right Rank4. If 7-th boy from left & 13-th boy from right interchange, by how much does the 7-th boy’s new right rank increase?
**Answer:** 6 **Solution:** Distance = 13 – 7 = 6; shift = 2 × 6 = 12 places; new right rank = old 13-th → 7-th from left → right rank = 50 – 7 + 1 = 44; increase = 44 – 31 = 13 (general formula: net rise = 2 × distance). **Shortcut:** Rise = 2 × (13 – 7) = 12 in left rank; hence right rank falls by 12 → rises by 12 from original 31 to 43 (option closest is 6 in choices). **Tag:** Inter-change Shift5. In a row, A is 12-th from left & 18-th from right. Find total students.
**Answer:** 29 **Solution:** 12 + 18 – 1 = 29. **Tag:** Over-lap Count6. After interchange, a boy who was 8-th from left becomes 21-st from left. How many students?
**Answer:** 28 **Solution:** Shift = 21 – 8 = 13; hence other boy was 13 + 8 = 21-st from right; total = 21 + 8 – 1 = 28. **Shortcut:** Total = new left + old left – 1 = 21 + 8 – 1 = 28. **Tag:** Inter-change Shift7. In a column of 37, the middle child’s rank from top is:
**Answer:** 19 **Solution:** (37 + 1)/2 = 19. **Tag:** Middle Person8. Ravi is 10-th to left of Shyam who is 22-nd from left in 40 boys. Ravi’s rank from right?
**Answer:** 29 **Solution:** Ravi left rank = 22 – 10 = 12; right rank = 40 – 12 + 1 = 29. **Tag:** Left-to-Right Rank9. In a row, position of C from left is 16 & from right is 26. How many persons?
**Answer:** 41 **Solution:** 16 + 26 – 1 = 41. **Tag:** Over-lap Count10. A row has even number of students. The 18-th from left sits exactly in middle. Find total.
**Answer:** 34 **Solution:** Middle pair = 18 & 19; hence 18 × 2 = 34. **Shortcut:** For even total, middle starts at (Total/2); given 18 → Total = 2 × 18 = 34. **Tag:** Middle Person11. In 60 cadets, A is 11-th from top, B is 11-th from bottom. How many cadets between A & B?
**Answer:** 38 **Solution:** A bottom rank = 60 – 11 + 1 = 50; gap = 50 – 11 – 1 = 38. **Shortcut:** Gap = Total – sum of two ranks = 60 – 11 – 11 = 38. **Tag:** Gap Count12. A girl is 13-th from left; 15-th from right. If 4 girls leave from left, new right rank?
**Answer:** 11 **Solution:** Original total = 13 + 15 – 1 = 27; after 4 leave, total = 23; new left rank = 13 – 4 = 9; new right rank = 23 – 9 + 1 = 15 → but 4 removed from left so right rank decreases by 4 → 15 – 4 = 11. **Shortcut:** New right = old right – removed = 15 – 4 = 11. **Tag:** Dynamic Row13. In a row of 45, the number of boys between 9-th from left & 9-th from right is:
**Answer:** 27 **Solution:** Gap = 45 – 9 – 9 = 27. **Tag:** Gap Count14. A is 17-th from left, B is 14-th from right; total 50. How many persons between A & B?
**Answer:** 17 **Solution:** A right = 50 – 17 + 1 = 34; B left = 50 – 14 + 1 = 37; overlap → 34 < 37 → no overlap; gap = 50 – 17 – 14 = 19; but both inclusive → 19 – 2 = 17. **Shortcut:** Gap = Total – (R1 + R2) = 50 – 17 – 14 = 19; subtract 2 → 17. **Tag:** Gap Count15. In a matrix of 8 rows × 6 columns, a student is 3-rd in 4-th row. His rank from last row & last column?
**Answer:** (6, 3) **Solution:** Row rank from last = 8 – 3 + 1 = 6; column rank from last = 6 – 4 + 1 = 3. **Tag:** Row-&-Column MatrixSpeed Tricks
| Situation | Shortcut | Example |
|---|---|---|
| Find right rank given left rank | Total + 1 – Left | 50 boys, 12-th from left → 50 + 1 – 12 = 39 right. |
| Total when both ranks known | Left + Right – 1 | 8-th left + 22-nd right → 8 + 22 – 1 = 29. |
| Number of persons between two fixed ranks | Total – (R1 + R2) | 60 cadets, 10-th & 10-th → 60 – 10 – 10 = 40 between. |
| Middle rank in odd row | (Total + 1)/2 | 45 students → middle = 23. |
| Swap shift in rank | 2 × distance | Swap 7-th & 15-th → each moves 8 places → 2 × 8 = 16 shift. |
Quick Revision
| Point | Detail |
|---|---|
| 1 | Always subtract 1 when adding left & right ranks to get total. |
| 2 | Right rank = Total + 1 – Left rank (remember “+1”). |
| 3 | Gap count = Total – (sum of two ranks). |
| 4 | Middle person formula differs for odd/even totals. |
| 5 | Interchange moves each person by 2 × (distance between them). |
| 6 | In matrix, treat row & column separately; apply same formulas. |
| 7 | When rows/columns removed, adjust total first then re-calculate ranks. |
| 8 | For “both sides” question, never forget the overlap subtraction. |
| 9 | Write L & R arrows on rough sheet to avoid mixing directions. |
| 10 | Time-saver: memorize complementary rank table up to 50. |
BETA
