Logical Reasoning : Ranking & Ordering
Ranking Formulas (Row/Line Positions):
- Total number of persons in a row:
- Total = (Left + Right) - 1
- Position from the right end:
- Right = (Total + 1) - Left
- Position from the left end:
- Left = (Total + 1) - Right
Q: If in a row, A’s position from the left is 15th and from the right is 25th, find the total number of persons in the row.
Soln:
Total = (Left + Right) - 1
= (15 + 25) - 1
= 40 - 1
= 39
Ans: 39 persons
Q: Seven friends — S, T, U, V, W, X, Y — have different ages.W is older than X but younger than V.Only three persons are older than W.T is older than U but younger than S.Y is the youngest. How many are younger than W ?
Soln:
If 3 are older than W → W is 4th in order.
Total = 7 → 7 − 4 = 3 younger than W.
Ans: 3 persons
Q: P, Q, R, S, and T have different heights.R is taller than T but shorter than P. S is taller than Q but shorter than T.Who among them is the talles ?
Soln:
R > T but < P ⇒ P > R > T
S > Q but < T ⇒ T > S > Q
Now combine both: P > R > T > S > Q
Ans: P is the tallest.
Q. In a row of ten boys, when Nitin was shifted two places to his left, he became 8th from the left end. What was his earlier position from the right end ?
Soln:
There are 10 boys in a row.
After moving 2 places left, Nitin becomes 8th from the left.
So before shifting, he was 2 places to the right → 10th from the left.
Now - since there are 10 boys total:
If he is 10th from the left, he is 1st from the right (same position).
So both are correct - they describe the same place.
10th from the left = 1st from the right.
Q: In a row of 35 students, when Siddhi moved 8 places to her right, she became 18th from the left end. What was her original position from the right end ?
Soln:
After moving 8 places right → new position from left = 18th
So, original position from left = 18−8=10th18 - 8 = 10th18−8=10th
Now, total students = 35
Position from right = 35−10+1=26th35 - 10 + 1 = 26th35−10+1=26th
Ans: 26th from the right end.
Q: In a row of students, Ram is 39th from the left end, while Shyam is 28th from the right end. If Ram and Shyam interchange their positions, Ram becomes 20th from the left. What will be Shyam’s new position from the right end ?
Soln:
Total students = (Ram’s new position from left) + (Shyam’s old position from right) − 1
= 20 + 28 − 1 = 47
Now, Shyam takes Ram’s old position = 39th from the left.
So, Shyam’s new position from the right = 47 − 39 + 1 = 9th
Ans: Shyam’s new position is 9th from the right.
Q: In a row of students, John is 16th from the left end, and Johnson is 8th from the right end. They interchange their positions. After changing positions, John becomes 33rd from the left end. How many students are there in the row?
Soln:
When they swap places, John’s new position from the left + Johnson’s original position from the right − 1 = total students
= 33 + 8 – 1 = 40
Ans: Total students = 40
Q: In a row, one person is 5th from the left and another is 25th from the right. If there are 6 persons between them, find:
(a) the maximum number of persons in the row, and
(b) the minimum number of persons in the row.
Soln:
Let’s understand,
- One person is 5th from the left.
- Another is 25th from the right.
- Between them = 6 persons.
(a) Maximum persons
Means they are not overlapping.
So, Total = 5 (left) + 6 (between) + 25 (right) = 36 persons
(b) Minimum persons
Means they are overlapping or same counted twice.
So, Total = 5 + 25 − 1 − 6 = 23 persons
Answer:
Maximum = 36
Minimum = 23
Why −1 ?
Because both positions count the same person once from each side, and we must correct for that duplication.
Q: In a class of 35 students, Karuna is 7th from the bottom and Surendra is 9th from the top. If Mohan is exactly in between them, then what is Karuna’s position from Mohan ?
Soln:
- Total students = 35
- Surendra is 9th from the top → so from the bottom he is 35 - 9 + 1 = 27th
- Karuna is 7th from the bottom
Now between Karuna (7th) and Surendra (27th):
27 - 7 - 1 = 19 students in between
Half of 19 = 9.5 ≈ 10
So Mohan is 10 students above Karuna.
Ans: Karuna is 10th below Mohan.
Q: In a row of 50 persons, A is 15th from the left end, and B is 19th from the right end. How many persons are there between A and B ?
Soln:
Total persons = 50
A is 15th from the left
B is 19th from the right
B’s position from left = 50 − 19 + 1 = 32
Persons between A and B = 32 − 15 − 1 = 16
Ans: 16 persons are between A and B.
Trick to Remember:
Persons between two = (Difference of their positions) - 1
So, (Bigger position - Smaller position) - 1
Q: In a class of 30 students, Mahesh is 14th from the left end and Ramesh is 20th from the right end. How many students are there between Mahesh and Ramesh ?
Soln:
Total students = 30
Ramesh’s position from left = 30 − 20 + 1 = 11th from left
Mahesh’s position from left = 14th
Students between them = 14 − 11 − 1 = 2
Ans: 2 students are between Mahesh and Ramesh.
Q: In a class of 60 students where the number of boys is double the number of girls, Kamal is 17th from the top. If there are 7 girls ahead of Kamal, how many boys are behind him ?
Soln:
Let the number of girls = x
Then, boys = 2x
Total = x + 2x = 3x = 60 → x = 20
So, girls = 20 and boys = 40
From top to Kamal’s position (17th),
Girls ahead = 7 → Boys ahead = 17 − 7 = 10
So, boys behind = 40 − 10 − 1 (Kamal himself) = 29
Ans: 29 boys are behind Kamal.
Q: In a class of 45 students, a boy’s rank is 20th from the top. When 2 more boys join, he moves one rank down.What is his new rank from the bottom ?
Soln:
- Original total students = 45
After 2 more join → New total = 45 + 2 = 47 - His new rank from top = 20 + 1 = 21st
- Rank from bottom = (Total students + 1) - (Rank from top)
= (47 + 1) - 21
= 48 − 21
= 27th from the bottom
Ans: The boy’s new position from the bottom is 27th.
Q: In a class, Shailesh is 7th from the top and Anupam is 18th from the bottom.
Suresh is 2 ranks above Anupam and 15 ranks below Shailesh. How many students are there in the class ?
Soln:
Anupam = 18th from bottom
→ Suresh = 18 + 2 = 20th from bottom
Shailesh = 7th from top
→ Suresh = 7 + 15 = 22nd from top
Total students = 22 + 20 − 1 = 41
Q: In a class of 40 students, Rita’s rank is 19th from the top. What is her rank from the bottom ?
Soln:
From bottom = (Total students + 1) − Top rank
= (40 + 1) − 19
= 41 − 19
= 22nd from the bottom
Q: Kamal’s position is 20th from the right in a row. There are 6 persons sitting between him and another person.
Find:
(i) The maximum number of persons in the row (normal case)
(ii) The minimum number of persons in the row (overlap case)
Soln:
(i) Maximum persons (Normal case): Total = 20 + 1 + 6 = 27
(If the other person is at the extreme left, all are counted normally)
(ii) Minimum persons (Overlap case): Total = 20 + 1 – 1 – 6 = 14
(Subtract 1 because Kamal and the other person are counted twice in overlap)
Ans:
- Maximum = 27
- Minimum = 14
Q: In a row of boys, Aman is 12th from the top and Baman is 18th from the bottom. If there are 6 boys between Aman and Baman, find the total number of boys in the row.
Soln:
Given:
- Aman = 12th from top
- Baman = 18th from bottom
- Boys between them = 6
Total boys formula when “between” is given:
Total = Position from top + Position from bottom + (boys between) - 1
Substitute: 12 + 18 + 6 – 1 = 35
Ans: 35
Q: Manoj is 16th from the top and 27th from the bottom in the passed list. 5 students didn’t appear, and 3 failed. Find total students.
Soln:
- Find the total passed students: Passed students = 16 + 27 – 1 = 42
- Include absent and failed students: Total students = 42 + 5 + 3 = 50
Ans: 50
Q: In a row, A is 15th from the left, and B is 10th from the right. B sits to the right of A, and there are 4 people between them. Find total number of people in the row.
Soln:
Let total number of people = N
Distance from left to B = A’s position + people between + 1 (for B itself)
= B’s position from left = 15 + 4 + 1 = 20
B's position from right = 10
Total people N = B’s position from left + B’s position from right – 1
N = 20 + 10 – 1 = 29
Ans: 29
Q: In a row, A is 15th from the left, and B is 10th from the right. B sits to the left of A, and there are 4 persons between them. How many persons are there in the row ?
Soln:
- A is 15th from left.
- B is 10th from right and sits left of A with 4 persons between them.
- So, B’s position from left = 15 − (4 + 1) = 10.
- Total students = B’s left position + B’s right position − 1 = 10 + 10 − 1 = 19..
Ans: 19 persons
Q: If in a row, B is 10th from the left and 16th from the right, then how many boys are there in the row ?
Soln:
- Total boys = (Position from left) + (Position from right) -1
- Total = 10 + 16 − 1 = 25
Ans: 25 boys
Q: In a row of 100 persons, A is 25th from the left. What is A’s position from the right ?
Soln:
- Total persons = 100
- Position from right = Total − Position from left + 1
- Position from right = 100 − 25 + 1 = 76
Ans: 76th from the right
Q: In a row, A’s position from the top is 20th. If in the same row, B’s position from the top is 15th and from the bottom is 25th, what is A’s position from the bottom ?
Soln:
- First, find the total number of students in the row using B’s position:
Total students = Position from top + Position from bottom - 1
Total students=15+25−1=39
2. Now, A’s position from the bottom:
Position from bottom = Total students − Position from top + 1
Position from bottom = 39 – 20 + 1 = 20
Ans: 20th from the bottom