Ranking refers to arranging people, objects, or events in a specific order based on position, performance, height, weight, age, or any other criterion.
| Scenario | Ranking Type | Example |
|---|---|---|
| Class Performance | Merit-based | Ram is 5th in class of 40 students |
| Height Arrangement | Physical attribute | Tallest to shortest in a line |
| Race Competition | Speed-based | Winner, 1st runner-up, 2nd runner-up |
| Age Comparison | Time-based | Oldest to youngest sibling |
| Benefit | Application |
|---|---|
| Logical Positioning | Understanding relative positions in sequences |
| Comparative Analysis | Comparing multiple elements simultaneously |
| Exam Relevance | Common in aptitude tests and competitive exams |
| Real-Life Skills | Queue management, scheduling, priority setting |
Understanding position from either end of a sequence.
| Formula | When to Use | Variables |
|---|---|---|
| Total = Rank from Top + Rank from Bottom - 1 | Finding total number | T = Total, Rt = Rank from top, Rb = Rank from bottom |
| Rank from Top = Total - Rank from Bottom + 1 | Finding rank from top | When total and bottom rank given |
| Rank from Bottom = Total - Rank from Top + 1 | Finding rank from bottom | When total and top rank given |
Problem: In a class, Ram ranks 7th from the top and 28th from the bottom. How many students are in the class?
Step-by-Step Solution:
| Step | Information | Calculation | Result |
|---|---|---|---|
| Given | Rank from top (Rt) | 7 | - |
| Given | Rank from bottom (Rb) | 28 | - |
| Formula | Total = Rt + Rb - 1 | 7 + 28 - 1 | 34 students |
| Why -1? | Ram is counted in both ranks | Avoid double counting | ✓ |
Visual Representation:
Top → 1, 2, 3, 4, 5, 6, [7-RAM], 8, 9, ... 27, 28 ← Bottom
←―――― 7 from top ――――→ RAM ←―――― 28 from bottom ――――→
Answer: 34 students ✅
Problem: In a row of 50 students, Sita is 12th from the top. What is her rank from the bottom?
Step-by-Step Solution:
| Step | Information | Calculation | Result |
|---|---|---|---|
| Given | Total students (T) | 50 | - |
| Given | Rank from top (Rt) | 12 | - |
| Formula | Rb = T - Rt + 1 | 50 - 12 + 1 | 39th from bottom |
| Verify | 12 + 39 - 1 | 50 | ✓ Correct |
Answer: 39th from bottom ✅
When positions change due to new arrangements.
Problem: In a queue of 40 people, Mohan is 16th from the front. If every alternate person from the front is removed, what will be Mohan's new position?
Step-by-Step Solution:
| Step | Original Position | Analysis | Result |
|---|---|---|---|
| Given | Mohan = 16th from front | Original position | - |
| Removal | 1st, 3rd, 5th, 7th, 9th, 11th, 13th, 15th removed | Every alternate from front | 8 people removed before Mohan |
| New Position | Original 16th position | 16 - 8 = 8 | 8th from front |
| Verify | Remaining: 2,4,6,8,10,12,14,[16-Mohan] | Count positions | ✓ 8th position |
Answer: 8th from front ✅
Understanding left and right positions in a straight line.
| Formula | Application | Example |
|---|---|---|
| Total = Left + Right - 1 | Finding total in row | Person is 5th from left, 8th from right |
| Left Position = Total - Right + 1 | Finding left position | Total 20, 6th from right = ? from left |
| Right Position = Total - Left + 1 | Finding right position | Total 30, 10th from left = ? from right |
Problem: In a row of children, Ajay is 9th from the left and 15th from the right. How many children are there?
Step-by-Step Solution:
| Step | Information | Calculation | Result |
|---|---|---|---|
| Given | Position from left | 9 | - |
| Given | Position from right | 15 | - |
| Formula | Total = L + R - 1 | 9 + 15 - 1 | 23 children |
Visual:
Left → 1,2,3,4,5,6,7,8,[9-Ajay],10,11,12,13,14,15,16,17,18,19,20,21,22,23 ← Right
←―― 9 from left ――→ AJAY ←―――――― 15 from right ――――――→
Answer: 23 children ✅
When two rows face each other, opposite positions matter.
Problem: Two rows of students are facing each other. Row 1 has 25 students, Row 2 has 25 students. If a student in Row 1 is 10th from the left, which position student from Row 2 is directly facing him from the right side of Row 2?
Step-by-Step Solution:
| Step | Analysis | Calculation | Result |
|---|---|---|---|
| Row 1 | 10th from left | Given | - |
| Row 2 | Facing arrangement | Mirror position | - |
| Logic | Same position number | If R1 is 10th from left, R2 facing = 10th from right | 10th from right |
| Formula | Position remains same | Direct opposite | ✓ |
Visual:
Row 1: 1 2 3 4 5 6 7 8 9 [10] 11 12 ... 25 (Left to Right)
↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕
Row 2: 25 24 23 22 21 20 19 18 17[16] 15 14 ... 1 (Right to Left)
Answer: 10th from right in Row 2 ✅
When rankings are based on scores, marks, or achievements.
Problem: In a class of 50 students:
Step-by-Step Solution:
| Step | Information | Calculation | Result |
|---|---|---|---|
| Given | A = 20th from top | Position A | - |
| Given | B = 25th from top | Position B | - |
| Positions | 20, 21, 22, 23, 24, 25 | Count between | - |
| Between A & B | 25 - 20 - 1 | Exclude A and B | 4 students |
Visual:
Rank: ... 20[A] 21 22 23 24 25[B] ...
↑ ↑
(4 students between them)
Formula: Students between = |Rank₁ - Rank₂| - 1
Answer: 4 students between A and B ✅
Arranging events, activities, or periods in chronological order based on time.
| Type | Description | Example |
|---|---|---|
| Day Sequence | Order of days in a week | Monday, Tuesday, Wednesday... |
| Month Sequence | Order of months in a year | January, February, March... |
| Event Sequence | Chronological order of events | Birth → School → College → Job |
| Age Comparison | Comparing ages of people | Oldest to youngest |
| Time Calculation | Finding past/future dates | What day was 3 days ago? |
| Day | Number | Position | Shorthand |
|---|---|---|---|
| Monday | 1 | 1st day | Mon |
| Tuesday | 2 | 2nd day | Tue |
| Wednesday | 3 | 3rd day | Wed |
| Thursday | 4 | 4th day | Thu |
| Friday | 5 | 5th day | Fri |
| Saturday | 6 | 6th day | Sat |
| Sunday | 7 | 7th day (or 0) | Sun |
| Formula | Application | Example |
|---|---|---|
| Days forward = Current day + n (mod 7) | Finding future day | Today is Monday, what day after 10 days? |
| Days backward = Current day - n (mod 7) | Finding past day | Today is Friday, what day 5 days ago? |
| Week cycle = 7 days | Repeating pattern | Every 7 days, same day repeats |
Problem: If today is Wednesday, what day will it be 25 days from now?
Step-by-Step Solution:
| Step | Information | Calculation | Result |
|---|---|---|---|
| Given | Today = Wednesday | Day 3 | - |
| Days ahead | 25 days | Given | - |
| Week calculation | 25 ÷ 7 | 3 weeks + 4 days | Remainder = 4 |
| New day | Wednesday + 4 days | Wed → Thu → Fri → Sat → Sun | Sunday |
Formula: (Current Day Number + Days Forward) mod 7
Calculation:
Wednesday = 3 25 days = 3 weeks (21 days) + 4 days 3 + 4 = 7 = Sunday (or Day 0)
Answer: Sunday ✅
Problem: If today is Saturday, what day was it 17 days ago?
Step-by-Step Solution:
| Step | Information | Calculation | Result |
|---|---|---|---|
| Given | Today = Saturday | Day 6 | - |
| Days ago | 17 days back | Given | - |
| Week calculation | 17 ÷ 7 | 2 weeks + 3 days | Remainder = 3 |
| Past day | Saturday - 3 days | Sat → Fri → Thu → Wed | Wednesday |
Calculation:
Saturday = 6 17 days ago = 2 weeks (14 days) + 3 days 6 - 3 = 3 = Wednesday
Answer: Wednesday ✅
| Month | Number | Days | Quarter |
|---|---|---|---|
| January | 1 | 31 | Q1 |
| February | 2 | 28/29 | Q1 |
| March | 3 | 31 | Q1 |
| April | 4 | 30 | Q2 |
| May | 5 | 31 | Q2 |
| June | 6 | 30 | Q2 |
| July | 7 | 31 | Q3 |
| August | 8 | 31 | Q3 |
| September | 9 | 30 | Q3 |
| October | 10 | 31 | Q4 |
| November | 11 | 30 | Q4 |
| December | 12 | 31 | Q4 |
| Months | Days | Memory Trick |
|---|---|---|
| 30 Days | Apr, Jun, Sep, Nov | "30 days has September, April, June, and November" |
| 31 Days | Jan, Mar, May, Jul, Aug, Oct, Dec | Use knuckle method (peaks = 31) |
| 28/29 Days | February only | Leap year = 29, Normal = 28 |
Problem: If March is the 3rd month, which month comes 5 months after March?
Step-by-Step Solution:
| Step | Information | Calculation | Result |
|---|---|---|---|
| Given | March = Month 3 | Starting point | - |
| Months ahead | 5 months | Given | - |
| Calculation | 3 + 5 | 8 | Month 8 |
| Month name | 8th month | August | August |
Answer: August ✅
Understanding relative ages and time gaps.
Problem:
Arrange them from oldest to youngest.
Step-by-Step Solution:
| Person | Age Relation | Relative Age | Rank |
|---|---|---|---|
| D | Youngest (base) | 0 years | 4th (Youngest) |
| C | D + 4 years | 4 years | 3rd |
| B | C + 2 years | 6 years | 2nd |
| A | B + 3 years | 9 years | 1st (Oldest) |
Visual Age Line:
D (0) → C (4) → B (6) → A (9) Youngest ←――――――――――――――→ Oldest
Answer: A B C D (Oldest to Youngest) ✅
| Step | Action | Details | Example |
|---|---|---|---|
| Step 1 | Identify Problem Type | Ranking (top/bottom), Row, Time, Age? | "7th from top, 28th from bottom" = Ranking |
| Step 2 | List Given Information | Write all positions, totals, dates | Total = ?, Rt = 7, Rb = 28 |
| Step 3 | Choose Correct Formula | Select appropriate formula | Total = Rt + Rb - 1 |
| Step 4 | Calculate Step-by-Step | Show each calculation clearly | 7 + 28 - 1 = 34 |
| Step 5 | Draw Diagram (if needed) | Visual representation helps | Draw number line with positions |
| Step 6 | Verify Answer | Check if answer makes logical sense | 7 + 28 - 1 = 34 ✓ |
| Q# | Question | Options |
|---|---|---|
| Q1 | In a class of 45 students, Ram ranks 15th from the top. What is his rank from the bottom? | A) 30brB) 31brC) 32brD) 29 |
Solution Table:
| Step | Given | Formula | Calculation |
|---|---|---|---|
| Total (T) | 45 students | - | - |
| Rank from top (Rt) | 15 | - | - |
| Rank from bottom (Rb) | ? | Rb = T - Rt + 1 | 45 - 15 + 1 = 31 |
Answer: B) 31 ✅
| Q# | Question | Options |
|---|---|---|
| Q2 | Mohan is 12th from the left and 18th from the right in a row. How many people are there? | A) 28brB) 29brC) 30brD) 31 |
Solution Table:
| Step | Information | Calculation | Result |
|---|---|---|---|
| Left position | 12 | Given | - |
| Right position | 18 | Given | - |
| Total | L + R - 1 | 12 + 18 - 1 | 29 |
Answer: B) 29 ✅
| Q# | Question | Options |
|---|---|---|
| Q3 | If today is Monday, what day will it be 16 days from now? | A) TuesdaybrB) WednesdaybrC) ThursdaybrD) Friday |
Solution Table:
| Step | Information | Calculation | Result |
|---|---|---|---|
| Today | Monday (Day 1) | - | - |
| Days forward | 16 days | 16 ÷ 7 = 2 weeks + 2 days | Remainder = 2 |
| New day | Monday + 2 | Mon → Tue → Wed | Wednesday |
Answer: B) Wednesday ✅
| Q# | Question | Options |
|---|---|---|
| Q4 | If today is Friday, what day was it 20 days ago? | A) MondaybrB) TuesdaybrC) SaturdaybrD) Sunday |
Solution Table:
| Step | Information | Calculation | Result |
|---|---|---|---|
| Today | Friday (Day 5) | - | - |
| Days back | 20 days | 20 ÷ 7 = 2 weeks + 6 days | Remainder = 6 |
| Past day | Friday - 6 | Fri → Thu → Wed → Tue → Mon → Sun → Sat | Saturday |
Answer: C) Saturday ✅
| Q# | Question | Options |
|---|---|---|
| Q5 | In a class, A ranks 10th from top and B ranks 15th from bottom. If there are 5 students between them, how many total students? | A) 28brB) 29brC) 30brD) 31 |
Solution Table:
| Step | Information | Analysis | Calculation |
|---|---|---|---|
| A from top | 10th | Given | - |
| B from bottom | 15th | Given | - |
| Between A & B | 5 students | Given | - |
| Total | A's rank + Between + B's rank | 10 + 5 + 15 | 30 students |
Answer: C) 30 ✅
| Q# | Question | Options |
|---|---|---|
| Q6 | If June 15th is a Monday, what day of the week is June 25th? | A) TuesdaybrB) WednesdaybrC) ThursdaybrD) Friday |
Solution Table:
| Step | Information | Calculation | Result |
|---|---|---|---|
| June 15 | Monday | Given | - |
| June 25 | ? | 25 - 15 = 10 days forward | - |
| Days calculation | 10 ÷ 7 | 1 week + 3 days | Remainder = 3 |
| New day | Monday + 3 | Mon → Tue → Wed → Thu | Thursday |
Answer: C) Thursday ✅
| Q# | Question | Options |
|---|---|---|
| Q7 | In a row of 60 people, A is 20th from left. After interchanging positions with B who is 30th from right, what is A's new position from left? | A) 30brB) 31brC) 32brD) 29 |
Solution Table:
| Step | Analysis | Calculation | Result |
|---|---|---|---|
| A's original | 20th from left | Given | - |
| B's original | 30th from right | Given | - |
| B's position from left | Total - Right + 1 | 60 - 30 + 1 = 31 | B is 31st from left |
| After interchange | A takes B's position | A moves to 31st from left | 31st from left |
Answer: B) 31 ✅
| Q# | Question | Options |
|---|---|---|
| Q8 | A is older than B by 5 years. B is younger than C by 3 years. If C is 25 years old, what is A's age? | A) 22brB) 23brC) 27brD) 28 |
Solution Table:
| Person | Age Relation | Calculation | Age |
|---|---|---|---|
| C | 25 years | Given | 25 |
| B | C - 3 years | 25 - 3 | 22 |
| A | B + 5 years | 22 + 5 | 27 |
Answer: C) 27 years ✅
| Q# | Question | Options |
|---|---|---|
| Q9 | In a merit list of 100 students, P is 15 ranks ahead of Q. If Q's rank is 40th from bottom, what is P's rank from top? | A) 45brB) 46brC) 47brD) 44 |
Solution Table:
| Step | Information | Calculation | Result |
|---|---|---|---|
| Total students | 100 | Given | - |
| Q from bottom | 40th | Given | - |
| Q from top | 100 - 40 + 1 | 61st from top | - |
| P is 15 ahead | Better rank (lower number) | 61 - 15 | 46th from top |
Answer: B) 46 ✅
| Q# | Question | Options |
|---|---|---|
| Q10 | If 1st January 2020 was a Wednesday, what day was 1st March 2020? (2020 is a leap year) | A) SaturdaybrB) SundaybrC) MondaybrD) Tuesday |
Solution Table:
| Step | Month | Days | Calculation |
|---|---|---|---|
| January | 1st to 31st | 31 days | - |
| February | 1st to 29th | 29 days (leap year) | - |
| Total days | Jan + Feb | 31 + 29 = 60 days | - |
| Weeks | 60 ÷ 7 | 8 weeks + 4 days | Remainder = 4 |
| Starting day | Wednesday | - | - |
| 1st March | Wed + 4 days | Wed → Thu → Fri → Sat → Sun | Sunday |
Answer: B) Sunday ✅
| What to Find | Formula | When to Use |
|---|---|---|
| Total | Rt + Rb - 1 | Given both ranks (top & bottom) |
| Rank from Top | T - Rb + 1 | Given total and rank from bottom |
| Rank from Bottom | T - Rt + 1 | Given total and rank from top |
| Students Between | |Rank₁ - Rank₂| - 1 | Finding gap between two ranks |
| Position in Row | L + R - 1 | Given left and right positions |
| Days Forward/Back | Action | Formula |
|---|---|---|
| Finding Future Day | Add days, divide by 7 | (Current day + Days) mod 7 |
| Finding Past Day | Subtract days, divide by 7 | (Current day - Days) mod 7 |
| Same Day Repeat | Every 7 days | Multiples of 7 = same day |
| Month Type | Months | Days | Memory Aid |
|---|---|---|---|
| 31 Days | Jan, Mar, May, Jul, Aug, Oct, Dec | 31 | Knuckle peaks |
| 30 Days | Apr, Jun, Sep, Nov | 30 | Between knuckles |
| Special | February | 28/29 | Leap year check |
| # | Tip | Why It Matters |
|---|---|---|
| 1 | 🔢 Remember the "-1" rule | Avoid double counting in rank formulas |
| 2 | 📊 Draw position diagrams | Visual aids prevent confusion |
| 3 | ⏰ Master the 7-day cycle | Every 7 days, same day repeats |
| 4 | 📅 Know month days by heart | Essential for date calculations |
| 5 | ✅ Always verify with formula | Check answer makes logical sense |
| 6 | 🎯 Identify problem type first | Ranking vs Time vs Age sequence |
| 7 | 📝 Write down all given info | Don't solve in head for complex problems |
| 8 | 🔄 Use remainder in day problems | Modulo 7 is your best friend |
| Mistake | Why It's Wrong | Correct Approach |
|---|---|---|
| Forgetting -1 in rank formula | Counts person twice | Always use Rt + Rb - 1 |
| Not using remainder | Wrong day calculation | Always divide by 7 and use remainder |
| Confusing left with right | Opposite positions | Draw diagram to clarify |
| Ignoring leap year | February has 29 days | Check if leap year (divisible by 4) |
| Adding instead of subtracting | Wrong direction in past days | Backward = subtract, Forward = add |
| Mixing up "between" | Including endpoints | Between = exclude both endpoints |
| Days Ahead | Shortcut | Example |
|---|---|---|
| 7, 14, 21, 28... | Same day | Monday + 14 days = Monday |
| 1 day | Next day | Monday + 1 = Tuesday |
| 6 days | Previous day | Monday + 6 = Sunday (one day before) |
| Rule | Condition | Example |
|---|---|---|
| Divisible by 4 | Leap year | 2020 ÷ 4 = 505 ✓ (Leap) |
| Century year | Must be divisible by 400 | 2000 ÷ 400 = 5 ✓ (Leap), 1900 ✗ (Not) |
| February days | 29 in leap, 28 in normal | 2020 = 29 days, 2021 = 28 days |
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