Ranking and Linear Arrangement
1. In a row of students, Ajay is 12th from the left and Vijay is 17th from the right. When Ajay and Vijay interchange their positions Vijay becomes 27th from the right. How many students are there between Vijay and Ajay?
a) 9 b) 12 c) 7 d) 10
Sol: From right end
i) Vijay’s present position: 27th
ii) Vijay’s former position: 17th
Now, total number of students between Ajay and Vijay = 27 − 17 − 1 = 9
2. Mouli is fourteenth from the right end in a row of 40 boys. What is his position from the left end?
a) 25th b) 27th c) 24th d) 26th
Sol: Mouli’s position from the left end = 40 + 1 − 14 = 27
3. In a row of boys, Jayati is seventh from the start and a eleventh from the end. In another row of boys, Bharat is tenth from the start and twelfth from the end. How many boys are there in both the rows together?
a) 36 b) 37 c) 39 d) None of these
Sol: Clearly, total number of boys in both the rows = (Number of boys in Jayati's row) + (Number of boys in Bharat's row)
= (6 + 1 + 10) + (9 + 1 + 11) = 17 + 21 = 38
4. Seema is 8 ranks ahead of Sajan, who ranks twenty-sixth in a class of 42. What is Seema’s rank from the last?
a) 9th b) 24th c) 25th d) 34th
Sol: Sajan rank 26th and Seema is 8 ranks ahead of Sajan. So, Seema ranks 18th.
Number of students behind Seema in rank = (42 - 18) = 24
So, Seema ranks 25th from the last.
5. In a row of girls facing North, Rajni is 10th to the left of Paro, who is 21st from the right end. If Meera, who is 17th from the left end, is fourth to the right of Rajni, how many girls are there in the row?
a) 37 b) 43 c) 44 d) Data inadequate
Sol: Here, Rajni’s position from the right end = 21 + 10 = 31
Meera’s position from the right end = 31 − 4 = 27
Meera’s position from the left end = 17th (given)
Thus, the total number of persons in the row = 27 + 17 − 1 = 43
6. Students line up in a queue in which Ashwani stands fifteenth from the left and Sandeep is seventh from the right. If they interchange their places, Sandeep would be fifteenth from the right. How many students are there in the queue?
a) 21 b) 22 c) 29 d) None of these
Sol: Sandeep’s new position is 15th from the right as well as from the left end of the row.
Number of students in the queue = (14 + 1 + 14) = 29
7. In a row of children, Hardipak is eleventh from the left and Manoj is seventeenth from the right. When they interchange their places, Hardipak will be thirteenth from the left. Which of the following will be the new position of Manoj from the right?
a) Eleventh b) Twenty-first c) Nineteenth d) Twenty-ninth
Sol: Manoj’s earlier position from the right end = 17
Manoj’s earlier position from the left end = 13
Total number of persons in the row = 17 + 13 − 1 = 29
Manoj’s new position from the right = 29 + 1 − 11 = 19
8. Neeta is taller than Sania. Neelima is taller than Neeta. Nitika is taller than Neelima. Mehak is the tallest of all. If they stand according to their height, who will be in the middle?
a) Neeta b) Neelima c) Sania d) Nitika
Sol: On the basis of the given information, we get
Mehak > Nitika > Neelima > Neeta > Sania
Obviously, Neelima will occupy the middle position.
9. In a team of five players, Vani is older than Rani. Sita is younger than Vani but older than Rani. Nita is younger than Mary and Rani. Rani is older than Mary. Whose age is middle of all the five in this team?
a) Vani b) Rani c) Sita d) Mary
Sol: Vani > Rani Vani > Sita > Rani Mary, Rani > Nita Rani > Mary
⇒ Vani > Sita > Rani > Mary > Nita
10. In a row of girls, Kamla is 9th from the left and Veena is 16th from the right. If they interchange their positions. Kamla becomes 25th from the left. How many girls are there in the row?
a) 34 b) 36 c) 40 d) 41
Sol: Kamal’s position from left = 9
Veena’s position from right = 16
After interchanging their positions,
Kamal’s position from left = 25
So, that Kamal’s position from right = 16
∴ Total number of girls = (25 + 16) − 1 = 40
11. In a class of boys Rajan got the 11th rank and he was 31st from the bottom of the list of boys passed. Three boys did not take the examination and one failed. What is the total strength of the class?
a) 32 b) 42 c) 45 d) 46
Sol: Rajan’s rank in the class = 11
Also, Rajan’s rank in the class from bottom = 31
∴ Number of boys passed = 41
Total number of boys = 41 + 31 + 1 = 45
12. B is twice as old as A but twice younger than F. C is half the age of A but is twice older than D. Who is the second oldest?
a) B b) F c) D d) C
Sol: B = 2A; F = 2B = 4A
A = 2C ⇒ C = A/2
C = 2D ⇒ D = C/2 = A/4
The correct order is F > B > A > C > D
Hence, the second oldest is B.
13. Five girls M, N, O, P and Q are standing in a row. P is on the right of Q, N is on the left of Q, but N is on the right of M, P is on the left of O. Who is standing on the extreme right end?
a) Q b) N c) O d) P
Sol: The given standing position is
Left ← M N Q P O → Right
14. Sita is elder than Swapna. Lavanya is elder than Swapna but younger than Sita. Suvarna is younger than both Hari and Swapna, Swapna is elder than Hari. Who is the youngest?
a) Sita b) Lavanya c) Suvarna d) Hari
Sol: The order of eldest to youngest is given below.
Sita > Lavanya > Swapna > Hari > Suvarna.
15. In a classroom, there are 5 rows, and 5 children A, B, C, D and E are seated one behind the other in 5 separate rows as follows:
A is sitting behind C, but in front of B.
C is sitting behind E.
D is sitting in front of E.
The order in which they are sitting from the first row to the last is
a) DECAB b) BACED c) ACBDE d) ABEDC
Sol: From the given information the order is DECAB
16. Suresh is 7 ranks ahead of Ashok in the class of 39 students. If Ashok’s rank is 17th from the last, what is Suresh’s rank from the start?
a) 16th b) 23rd c) 24th d) 15th
Sol: Ashok's rank from last = 17
∴ Suresh's rank from last = 17 + 7 = 24
∴ Suresh's rank from the start = 39 − 24 + 1 = 16
17. A goldsmith has five rings. Each having a different weight.
Ring D weighing twice as much as Ring E.
Ring E weighing four and one-half times as much as Ring F.
Ring F weighing half as much as Ring G.
Ring G weighing half as much as Ring H.
Ring H weighing less than Ring D but more than Ring F.
Which of the following represents the descending order of weights of the rings?
a) D, E, G, H, F b) D, E, F, H, G c) E, G, H, D, F d) D, E, H, G, F
Sol: Let weight of the ring D be x gm.
∴ Weight of E = x/2 gm.
Weight of F = x/2 × 2/9 = x/9 gm.
Weight of G = 2x/9 gm.
Weight of H = 2x/9 gm.
Weight of D > Weight of H > Weight of F
∴ Descending order of weight of the rings D > E > H > G > F
18. Rahul is taller than Saurav, Sachin is taller than Rahul and Dhoni is taller than Kaif but shorter than Saurav. Who is the tallest?
a) Sachin b) Rahul c) Dhoni d) Saurav
Sol: The order of the heights of the persons according to the given information will be
Sachin > Rahul > Saurav > Dhoni > Kaif
Hence, Sachin is the tallest.
19. Five books are lying in a pile. E is lying on A, C is lying under B, A is lying above B, and D is lying under C. Which book is lying at the bottom?
a) A b) B c) C d) D
Order And Ranking
Order and ranking is an important chapter of reasoning section for all competitive exam particularly bank exams. In this article, we will discuss important concepts of order and ranking concepts with simple logical methods and tips i.e, with out formulae also we can answer these questions very easily if you understand the basic concepts.
1. RANKING TYPE
2. COMPARISON TYPE
RANKING TYPE: In this type, the data related to ranks of a person/ persons from the left side/ right side/ top/ bottom are given and the total number of persons are asked. In some questions, the total number of persons are given and rank of the person from left side/ right side/ top/ bottom are asked. So different types of questions can be formed based on the rank/ position of the persons in a row.
Note: consider your Left-hand side as the Left side and your Right hand as the Right side.
CASE 1: To find the position of a person from opposite side, when rank from one side and total number of persons are given. Ex: in a row of 49 persons, position of Rani from right end of the row is 25th. What is the position of Rani from the Left end of the row? Sol: (49 - 25) + 1 = 23
In this case to find Rani's position from left end we have to subtract rani's right end value from total (49 - 25) = 24, that resultant value is not correct because that 24 is total persons before or left side of Rani but it is not included Rani's position, so to find Rani's position form another end we have to add 1 then we will get correct position of Rani from Left end.
Note: At what situation we have to add 1 & why we are adding 1, we have to remember that.
ASE 2: To find the total number of persons, when ranks of one person is given from both sides of the row.
Ex: in a row of persons, position of Nithya is 32nd from the left end of the row and 29th from the right end of the row. Then find the total number of the persons in the row?
Sol: (32 + 29) - 1 = 60
In this case same person is counting two time (in 29 & 32) so we have to subtract 1 after adding both the end values to get actual total.
Note: At what situation we have to subtract 1 & why we are subtracting 1, we have to remember that.
CASE 3: To find the total number of persons between any two persons in that row, when total number of persons and positions of both the persons (one from left end side and another person is from right end side) are given.
i. Not overlapping case: When total number of persons > (Left end position + Right end position)
Ex: In a row of 85 persons, position of Naveen is 34th from the left end and position of Raju is 29th from the right end, then find the total number of persons between Naveen and Raju?
Sol: 85 - (34 + 29) = 22
ii. Overlapping case: When (Left end position + Right end position) > total number of persons. Ex: In a row of 62 persons, Riya is 36th from the left end and Raman is 29th from the right end of the row. Then find the total number of persons setting between them
Sol: (36 + 29) - 62 - 2 = 1
CASE 4: When in a row, the positions of two persons are given and their positions are interchanged and after interchanging the position of 1st/ 2nd person is given from the same side as before interchanging.
Ex: In a row of girls, Pratibha is 15th from the left end and Kanika is 23rd from end. If they interchange their positions, then Pratibha becomes 18th from the left end. Find the position of Kanika from the right end?
Sol: Total no.of girls = (23 + 18) - 1 = 40
Kanika's position from right end = (40 - 15) + 1 = 26
Ex: In a row of students, Arjun 12th from left end and Anji is 18th from the right end of the row. If they interchanged their positions, Anji becomes 29th from right end. Find
i. New position of Arjun from the right end
ii. Total number of students
iii. Number of students between them
Sol: i. 18 ii. (29 + 12) - 1 = 40
iii. 40 - (12 + 18) = 10
CASE 5: If total number of persons are asked and positions of two different positions from different sides are given then it is always a case of ‘cannot be determined’. Because we do not know if there will be overlapping or not.
Ex: In a row of boys, position of Raman is 22nd from left end and position of Ramesh is 35th from right end. Find the total number of boys in the row?
Sol: Cannot be determined
1. Ravi is 7 ranks ahead of Sumit in a class of 39. If Sumit's rank is seventeenth from the last, what is Ravi's rank from the start?
a) 14th b) 15th c) 16th d) 17th e) 18th
Explanation: So, Ravi is 24th form the last. Number of students ahead of Ravi in rank
= (39 - 24) = 15
So, Ravi is 16th from the start.
2. In a row of girls, Rita and Monika occupy the ninth place from the right end and tenth place from the left end, respectively. If they interchange their places, then Rita and Monika occupy seventeenth place from the right end and eighteenth place from the left end respectively. How many girls are there in the row?
a) 25 b) 26 c) 27 d) Data inadequate e) None of these
Explanation: Number of girls in the row
= (16 + 1 + 9) = 26
3. In a row of 40 girls, when Kanika was shifted to her left by 4 places her number from the left end of the row became 10. What was the number of Swati from the left end of the row if Swati was three places to the right of Kanika's original position?
a) 18 b) 20 c) 19 d) 21 e) None of these
Explanation: Swati is 3 places to the right of Kanika's original position. Clearly, Swati is 17th from the left end.
4. In a row of girls facing North, Reena is 10th to the left of Pallavi, who is 21st from the right end. If Malini, who is 17th form the left end, is fourth to the right of Reena, how many girls are there in the row?
a) 37 b) 43 c) 44 d) 40 e) Data inadequate
Explanation: Pallavi is 21st from right and Reena is 10th to the left of Pallavi. So, Reena is 31st from right.
Malini is 4th to the right of Reena. So, Malini is 27th from the right. Also, Malini is 17th from the left.
∴ Number of girls in the row
= (26 + 1 + 16) = 43
5. In a row of girls, Kamya is fifth from the left and Preeti is sixth from the right. When they exchange their positions, then Kamya becomes thirteenth from the left. What will be Preeti's position from the right?
a) 7th b) 11th c) 14th d) 19th e) 18th
Explanation: Thus, the row consists of (12 + 1 + 5) = 18 girls.
Now, Preeti's new position is Kamya's earlier position which is 5th from the left.
Number of girls to the right of Preeti
= (18 − 5) = 13
So, Preeti's new position is 14th from the right.
6. Akash ranks seventh from the top and twenty-sixth from the bottom in a class. How many students are there in the class?
a) 31 b) 32 c) 33 d) 34 e) 35
Explanation: Clearly, the whole class consists of: So, total students
= (6 + 1 + 25) = 32 students
7. If Atul finds that he is twelfth from the right in a line of boys and fourth from the left, how many boys should be added to the line such that there are 28 boys in the line?
a) 12 b) 13 c) 14 d) 19 e) 20
Explanation: Clearly, number of boys in the line = (11 + 1 + 3) = 15
∴ Number of boys to be added = (28 - 15) = 13
8. Rohit is seventeenth from the left end of a row of 29 boys and Karan is seventeenth from the right end in the same row. How many boys are there between them in the row?
a) 3 b) 5 c) 6 d) 7 e) Data inadequate
Explanation: Total number of boys = 29
Number of boys to the left of Karan = (29 − 17) = 12
So, Karan is 13th from the left end. Also, Rohit is 17th from the left end.
Clearly, there are 3 boys between Rohit and Karan.
9. In a class of 60, where girls are twice that of boys, Kamal ranked seventeenth from the top. If there are 9 girls ahead of Kamal, how many boys are after him in rank?
a) 3 b) 7 c) 12 d) 19 e) 23
Explanation: Let the number of boys be x. Then, number of girls = 2x
∴ x + 2x = 60 or 3x = 60 or x = 20
So, number of boys = 20
and number of girls = 40
Number of students behind Kamal in rank = (60 - 17) = 43
Number of girls ahead of Kamal in rank = 9
Number of girls behind Kamal in rank = (40 - 9) = 31
∴ Number of boys behind Kamal in rank = (43 - 31) = 12
10. In a row of boys, A is thirteenth from the left and D is seventeenth from the right. If in this row A is eleventh form the right then what is the position of D from the left?
a) 6th b) 7th c) 10th d) 11th e) 12th
Explanation: So, number of boys in the row = (12 + 1 + 10) = 23
Now, D is 17th from the right D’s position from left = (23 - 16) = 7th
11. Forty boys are standing in a row facing the North. Amit is eleventh from the left and Deepak is thirty-first from the right end of the row. How far will Shreya, who is third to the right of Amit in the row, be from Deepak?
a) 2nd b) 3rd c) 4th d) 5th e) 6th
Explanation: Number of boys to the left of Deepak = (40 - 31) = 9
So, Deepak is 10th from the left end.
Sherya is third to the right of Amit.
So Shreya is 14th from the left end Clearly, Shreya is fourth to the right of Deepak.
In this type of order and ranking questions, candidates need to compare different quantities to determine correct order. Age, marks, height and weight etc have to compare according to given clues.
1. Among B, F, J, K and W, each one of them is of different heights, F is taller than only J. B is taller than F and W (both) but not as tall as K. Who among them is the third tallest?
a) B b) F c) K d) W e) None of these
Explanation: K > B > W > F > J
2. Among A, B, C, D and E, A is taller than only B but shorter than C. C is taller than E. C is not the tallest. Who among them will be in the middle if they stand in the order of their height?
a) A b) C c) B d) D e) None of these
Explanation: D > C > E > A > B
3. Among P, Q, R, S and T, each of them is of different weights, Q is lighter than only T. P is heavier than only S. Who will be second heaviest among the following?
a) R b) S c) T d) Q e) None of these
Explanation: T > Q > R > P > S
4. P, Q, R, S, T, U are having different toffees. P have more toffees than only S and T both but less than Q. R has more toffees than U but less than Q. Who among them have least number of toffees?
a) R b) S c) T d) Either b or c e) None of these
Explanation: Q > R > U > P > S/T > S/T
5. Among P, Q, R, S, T and U; R is shorter than only P and U. S is shorter than T and Q. If each of them is of different heights, who among them will be the shortest?
a) U b) P c) S d) Q e) R
Explanation: P/U > P/U > R > T/Q > T/Q > S
Directions (Qs. 6 - 8): Study the following information carefully and answer the given questions. Amongst five friends A, B, C, D, E each got different marks in the examination. A scored more than B but less than C. C scored 65 marks. D scored less marks than only E. The one who scored the minimum marks scored 60 marks and the one who scored the highest, scored 80 marks.
6. Who scored the second highest marks?
a) B b) E c) D d) C e) A
7. Who is the most likely to have scored 62 marks?
a) B b) A c) D d) E e) Either E or B
8. Who scored the lowest marks?
a) B b) E c) D d) C e) A
Directions (Qs. 9 - 11): Study the following information carefully and answer the questions given below: There are six persons who all are of different height. A is taller than C and D but shorter than E. The one who is third shortest is 102 cm in height. B is taller than A. E is not the tallest. The one who is second tallest is 119 cm in height. Neither A nor C is the third shortest person among all. C is not the shortest among all. F is taller than D.
9. Who among the following is the second tallest?
a) F b) E c) A d) C e) None of these
10. What will be the possible height of A?
a) 120 cm b) 100 cm c) 112 cm d) 101 cm e) None of these
11. Who among the following is third shortest? |
a) A b) C c) B d) F e) None of these
12. There are five persons i.e. P, Q, R, S and T. If Q is taller than R and S but smaller than T. S is smaller than T, who is not the tallest. Then who is the tallest person among all?
a) T b) Q c) S d) P e) None of these
Explanation: P > T > Q > R/S > R/S
Directions (Qs. 13 - 15): Read the following information carefully to answer the given questions. There are six persons S, T, U, V, W and X who got different marks in the examination. S got more marks than only U and X. T got less marks than W, who did not get the highest marks in the examination. The Second highest person got 92 marks.
13. How many persons got more marks than U?
a) Four b) Two c) Five d) Can’t be determined e) One
14. If S got 69 marks and U got 65 marks, then which of the following statement is true?
a) X got the lower marks
b) U got the fifth highest marks
c) Five persons got more marks than X
d) All are true
e) X got 67 marks is a possibility
15. V got which of the following possible score?
a) 85 b) 66 c) 92 d) 89 e) 94
Explanation: V > W > T > S > U/X > U/X 92
Directions (Qs. 16 - 20): Study the following information carefully and answer the questions given below: Seven persons are buying different things. Only one person buy thing between C and A. B is buying thing immediately before C. Two persons buy things between C and D. C buy things after D. E buys thing immediately before D. More than three persons buy things between E and F. Only three persons buy things between D and G.
16. How many persons buy things between A and F?
a) One b) Two c) Three d) Four e) More than four
17. Who among the following buy thing immediately after F?
a) D b) B c) G d) A e) No one
18. Who among the following buy thing immediately before G?
a) D b) B c) C d) A e) No one
19. How many persons buy things before A?
a) One b) Two c) Three d) Four e) More than four
20. As many as persons are buying things before D as after.......?
a) E b) B c) F d) A e) G
Explanation: E > D > A > B > C > G > F
21. Among five friends P, Q, R, S and T; Q is taller than R. T is taller than P. S is shorter than P but taller than Q. Who among them is the second shortest?
a) T b) Q c) R d) P e) Cannot be determined
Explanation: T > P > S > Q > R
22. At Banjara hills, there are 6 buildings U, V, W, X, Y and Z having different heights. Building V is taller than building Y, which is not taller than building W. building X is shorter than building U but taller than building Z. Building Y is taller than building X but building V is not the tallest. W is shorter than only 2 buildings. Which building is second tallest?
a) U b) V c) W d) Y e) Cannot be determined
Explanation: U > V > W > Y > X > Z
23. M, N, O, P, Q and R, when arranged in descending order of their weight from top, Q becomes third heaviest, R is between M and Q, O and P are neither at top(heaviest) nor at last (lightest). Who among them is the second heaviest according to their weight?
a) M b) O c) P d) N e) R
Explanation: M > R > Q > O/P > O/P > N
24. Six students U, V, W, X, Y and Z participate in an examination and score different marks. Z scores more than V but less than W. Y scores more than W but he does not score the highest marks. V scores more than only U. Who scores the second highest marks? a) U b) Y c) X d) Z e) None of these
Explanation: X > Y > W > Z > V > U
25. Among Q, P, L, M and N, each score different marks. P scores more than only L and N and less than M and Q. Who scores the highest marks?
a) Q b) M c) N d) Data inadequate e) None of these
Explanation: M/Q > M/Q > P > L/N > L/N