Convert verbal positions into numbers

If a person is r-th from the left in a row of N people, the same person is (N−r+1)-th from the right. The +1 matters because the person is included from both ends. For example, the 8th from the left in a row of 25 is 18th from the right: 25−8+1=18. If one person is 7th from the left and 12th from the right, the total is 7+12−1=18.

Put the row on a number line

For relative positions, assign positions from the left: 1, 2, 3 and so on. If A is 6th from the left and B is three places to A's right, B is 9th from the left. “Three persons between A and B” means their position numbers differ by four, not three. In facing-direction questions, distinguish the row's left from a person's left. A row facing south reverses the left/right seen by a north-facing observer.

Tallest, oldest and score rankings

Rankings use the same mathematics as row positions, but the order may be decreasing rather than left to right. Define rank 1 as highest or lowest according to the stem. If A is 5th highest among 20 candidates, 15 candidates are below A. Between two known ranks 5 and 11 are 5 people, because 11−5−1=5. Do not substitute the difference 6 for the number strictly between them.

Consistency check

The converted rank must lie between 1 and N. If two clues place the same person at inconsistent positions, revisit whether one clue was from the other end. For a group with no stated total, solve it from two-end information before placing others. In a timed paper, write a quick row with endpoints L and R, and annotate each named person once. This is more reliable than repeatedly recomputing the same relationship in prose.

Practice — 50 questions

Attempt every item before reading the answers below. Figure questions require the printed or on-screen diagram.

1. In a row of candidates in an exam, Sneha is 19th from the left and Kavita is 28th from the left. How many candidates in an exam are there between Sneha and Kavita?

A. 11 B. 9 C. 5 D. 8

2. In a row of candidates in an exam, Vikram is 13th from the left and Meena is 22nd from the left. How many candidates in an exam are there between Vikram and Meena?

A. 5 B. 8 C. 9 D. 11

3. In a group of 45 runners in a race, Priya ranks 6th from the top. What is Priya's rank from the bottom?

A. 39 B. 43 C. 41 D. 40

4. In a row of runners in a race, Pooja is 7th from the left and Sanjay is 14th from the left. How many runners in a race are there between Pooja and Sanjay?

A. 9 B. 4 C. 3 D. 6

5. In a row of 26 girls facing north, Aman is 20th from the left end. If Sneha is 9th to the left of Aman, what is Sneha's position from the right end?

A. 16th B. 15th C. 18th D. 17th

6. Priya is 19th from the top and 21st from the bottom among candidates in an exam. How many candidates in an exam are there in total?

A. 39 B. 40 C. 38 D. 41

7. In a row of people standing in a queue, Divya is 20th from the left and Arjun is 34th from the left. How many people standing in a queue are there between Divya and Arjun?

A. 15 B. 13 C. 10 D. 11

8. Suresh is 9th from the top and 25th from the bottom among runners in a race. How many runners in a race are there in total?

A. 33 B. 30 C. 31 D. 32

9. Karan is 21st from the top and 16th from the bottom among students in a class. How many students in a class are there in total?

A. 37 B. 36 C. 39 D. 34

10. In a row of people standing in a queue, Divya is 4th from the left and Suresh is 11th from the left. How many people standing in a queue are there between Divya and Suresh?

A. 8 B. 6 C. 9 D. 3

11. In a group of 41 runners in a race, Kavita ranks 9th from the top. What is Kavita's rank from the bottom?

A. 33 B. 32 C. 34 D. 31

12. In a row of 37 people facing north, Rohit is 29th from the right end. If Sneha is 10th to the right of Rohit, what is Sneha's position from the left end?

A. 21st B. 20th C. 18th D. 19th

13. In a row of candidates in an exam, Meena is 7th from the left and Sanjay is 14th from the left. How many candidates in an exam are there between Meena and Sanjay?

A. 6 B. 4 C. 5 D. 8

14. Sanjay is 23rd from the top and 20th from the bottom among runners in a race. How many runners in a race are there in total?

A. 43 B. 45 C. 42 D. 41

15. In a row of 37 children facing north, Neha is 21st from the right end. If Sneha is 5th to the right of Neha, what is Sneha's position from the right end?

A. 16th B. 17th C. 15th D. 26th

16. In a row of 49 people facing north, Sanjay is 46th from the left end. If Rahul is 16th to the left of Sanjay, what is Rahul's position from the right end?

A. 22nd B. 19th C. 21st D. 20th

17. In a group of 89 candidates in an exam, Anjali ranks 53rd from the top. What is Anjali's rank from the bottom?

A. 34 B. 37 C. 38 D. 40

18. In a group of 72 candidates in an exam, Pooja ranks 29th from the top. What is Pooja's rank from the bottom?

A. 44 B. 41 C. 47 D. 43

19. In a row of 53 students facing north, Anjali is 25th from the left end. If there are 16 students between Anjali and Vikram, with Vikram to the right of Anjali, what is Vikram's position from the left end?

A. 11th B. 42nd C. 41st D. 43rd

20. In a row of 32 people facing north, Sneha is 18th from the left end. If Neha is 4th to the right of Sneha, what is Neha's position from the right end?

A. 12th B. 19th C. 11th D. 10th

21. In a row of 46 children facing north, Vikram is 10th from the left end. If there are 18 children between Vikram and Pooja, with Pooja to the right of Vikram, what is Pooja's position from the left end?

A. 30th B. 17th C. 29th D. 28th

22. Rahul is 38th from the top and 34th from the bottom among runners in a race. How many runners in a race are there in total?

A. 74 B. 73 C. 71 D. 69

23. Kavita ranks 12th from the top among 41 candidates in an exam. If 6 more candidates in an exam join the bottom of the row, and Kavita's position relative to the others stays the same, what is Kavita's new rank from the bottom?

A. 36 B. 38 C. 37 D. 39

24. In a group of 71 players in a tournament, Suresh ranks 69th from the top. What is Suresh's rank from the bottom?

A. 4 B. 2 C. 1 D. 3

25. Rohit is 32nd from the top and 12th from the bottom among players in a tournament. How many players in a tournament are there in total?

A. 41 B. 40 C. 42 D. 43

26. In a row of 31 boys facing north, Sanjay is 6th from the left end. If there are 15 boys between Sanjay and Kavita, with Kavita to the right of Sanjay, what is Kavita's position from the left end?

A. 9th B. 23rd C. 21st D. 22nd

27. In a row of 35 soldiers facing north, Priya is 21st from the left end. If Anjali is 12th to the right of Priya, what is Anjali's position from the left end?

A. 2nd B. 34th C. 9th D. 33rd

28. In a row of 25 children facing north, Anjali is 17th from the right end. If Aman is 4th to the left of Anjali, what is Aman's position from the right end?

A. 22nd B. 20th C. 21st D. 13th

29. In a row of 54 people facing north, Divya is 50th from the left end. If Priya is 14th to the left of Divya, what is Priya's position from the left end?

A. 37th B. 36th C. 18th D. 35th

30. In a row of students in a class, Anjali is 12th from the left and Divya is 37th from the left. How many students in a class are there between Anjali and Divya?

A. 22 B. 21 C. 26 D. 24

31. Divya ranks 20th from the top among 51 players in a tournament. If 5 more players in a tournament leave from the top of the row, and Divya's position relative to the others stays the same, what is Divya's new rank from the bottom?

A. 32 B. 31 C. 30 D. 33

32. In a row of candidates in an exam, Sneha is 19th from the left and Kavita is 47th from the left. How many candidates in an exam are there between Sneha and Kavita?

A. 28 B. 24 C. 27 D. 30

33. Kavita ranks 37th from the top among 55 players in a tournament. If 4 more players in a tournament join the bottom of the row, and Kavita's position relative to the others stays the same, what is Kavita's new rank from the bottom?

A. 22 B. 25 C. 23 D. 24

34. Aman is 36th from the top and 10th from the bottom among people standing in a queue. How many people standing in a queue are there in total?

A. 45 B. 42 C. 47 D. 48

35. Divya ranks 11th from the top among 39 candidates in an exam. If 6 more candidates in an exam join the bottom of the row, and Divya's position relative to the others stays the same, what is Divya's new rank from the bottom?

A. 38 B. 35 C. 33 D. 34

36. Rahul is 14th from the top and 35th from the bottom among candidates in an exam. How many candidates in an exam are there in total?

A. 47 B. 50 C. 51 D. 48

37. In a row of 41 children facing north, Divya is 19th from the left end. If there are 15 children between Divya and Neha, with Neha to the right of Divya, what is Neha's position from the left end?

A. 34th B. 6th C. 36th D. 35th

38. Arjun is 38th from the top and 11th from the bottom among people standing in a queue. How many people standing in a queue are there in total?

A. 48 B. 51 C. 45 D. 47

39. In a group of 64 students in a class, Priya ranks 45th from the top. What is Priya's rank from the bottom?

A. 18 B. 20 C. 23 D. 22

40. In a row of 56 children facing north, Priya is 17th from the right end. If there are 12 children between Priya and Pooja, with Pooja to the left of Priya, what is Pooja's position from the right end?

A. 31st B. 30th C. 4th D. 29th

41. In a row of people standing in a queue, Pooja is 10th from the left and Neha is 46th from the left. How many people standing in a queue are there between Pooja and Neha?

A. 36 B. 38 C. 37 D. 35

42. Kavita is 52nd from the top and 38th from the bottom among students in a class. How many students in a class are there in total?

A. 91 B. 89 C. 87 D. 92

43. In a row of people standing in a queue, Kavita is 11th from the left and Suresh is 29th from the left. How many people standing in a queue are there between Kavita and Suresh?

A. 17 B. 16 C. 14 D. 19

44. In a row of 72 children facing north, Karan is 54th from the left end. If Divya is 12th to the right of Karan, what is Divya's position from the left end?

A. 6th B. 42nd C. 67th D. 66th

45. In a row of 71 girls facing north, Priya is 66th from the left end. If Neha is 8th to the left of Priya, what is Neha's position from the right end?

A. 16th B. 14th C. 15th D. 13th

46. Sneha is 26th from the top and 58th from the bottom among candidates in an exam. How many candidates in an exam are there in total?

A. 82 B. 83 C. 85 D. 81

47. In a row of 48 boys facing north, Karan is 10th from the right end. If Pooja is 11th to the left of Karan, what is Pooja's position from the right end?

A. 23rd B. 20th C. 21st D. 22nd

48. In a row of 77 people facing north, Divya is 67th from the left end. If there are 7 people between Divya and Neha, with Neha to the left of Divya, what is Neha's position from the right end?

A. 20th B. 18th C. 3rd D. 19th

49. Sneha ranks 44th from the top among 63 runners in a race. If 6 more runners in a race join the bottom of the row, and Sneha's position relative to the others stays the same, what is Sneha's new rank from the bottom?

A. 25 B. 26 C. 29 D. 23

50. In a row of students in a class, Arjun is 16th from the left and Karan is 49th from the left. How many students in a class are there between Arjun and Karan?

A. 32 B. 30 C. 35 D. 29

Answers and explanations

After checking the key, explain the rule or diagram transformation to yourself before moving on.

1. D. Number of people strictly between the two ranks = |28 − 19| − 1 = 8.

APRS26-08-01 | People between two ranks | Easy

2. B. Number of people strictly between the two ranks = |22 − 13| − 1 = 8.

APRS26-08-02 | People between two ranks | Easy

3. D. Rank from bottom = Total − Rank from top + 1 = 45 − 6 + 1 = 40.

APRS26-08-03 | Rank conversion | Easy

4. D. Number of people strictly between the two ranks = |14 − 7| − 1 = 6.

APRS26-08-04 | People between two ranks | Easy

5. A. Aman is 20th from the left, i.e. position 20 from the left. Facing north, "left" means towards the left end, so Sneha is at 20 − 9 = 11 from the left. From the right end: 26 − 11 + 1 = 16.

APRS26-08-05 | Position via relative offset | Easy

6. A. Total = (Rank from top) + (Rank from bottom) − 1 = 19 + 21 − 1 = 39.

APRS26-08-06 | Total from two ranks | Easy

7. B. Number of people strictly between the two ranks = |34 − 20| − 1 = 13.

APRS26-08-07 | People between two ranks | Easy

8. A. Total = (Rank from top) + (Rank from bottom) − 1 = 9 + 25 − 1 = 33.

APRS26-08-08 | Total from two ranks | Easy

9. B. Total = (Rank from top) + (Rank from bottom) − 1 = 21 + 16 − 1 = 36.

APRS26-08-09 | Total from two ranks | Easy

10. B. Number of people strictly between the two ranks = |11 − 4| − 1 = 6.

APRS26-08-10 | People between two ranks | Easy

11. A. Rank from bottom = Total − Rank from top + 1 = 41 − 9 + 1 = 33.

APRS26-08-11 | Rank conversion | Easy

12. D. Rohit is 29th from the right, so from the left Rohit is at 37 − 29 + 1 = 9. Facing north, "right" means towards the right end, so Sneha is at 9 + 10 = 19 from the left. So Sneha's position from the left end is 19.

APRS26-08-12 | Position via relative offset | Easy

13. A. Number of people strictly between the two ranks = |14 − 7| − 1 = 6.

APRS26-08-13 | People between two ranks | Easy

14. C. Total = (Rank from top) + (Rank from bottom) − 1 = 23 + 20 − 1 = 42.

APRS26-08-14 | Total from two ranks | Easy

15. A. Neha is 21st from the right, so from the left Neha is at 37 − 21 + 1 = 17. Facing north, "right" means towards the right end, so Sneha is at 17 + 5 = 22 from the left. From the right end: 37 − 22 + 1 = 16.

APRS26-08-15 | Position via relative offset | Easy

16. D. Sanjay is 46th from the left, i.e. position 46 from the left. Facing north, "left" means towards the left end, so Rahul is at 46 − 16 = 30 from the left. From the right end: 49 − 30 + 1 = 20.

APRS26-08-16 | Position via relative offset | Medium

17. B. Rank from bottom = Total − Rank from top + 1 = 89 − 53 + 1 = 37.

APRS26-08-17 | Rank conversion | Medium

18. A. Rank from bottom = Total − Rank from top + 1 = 72 − 29 + 1 = 44.

APRS26-08-18 | Rank conversion | Medium

19. B. Anjali is 25th from the left, i.e. position 25 from the left. 16 people between them means Vikram is 17 places to the right: 25 + 17 = 42 from the left. So Vikram's position from the left end is 42.

APRS26-08-19 | Position via relative offset | Medium

20. C. Sneha is 18th from the left, i.e. position 18 from the left. Facing north, "right" means towards the right end, so Neha is at 18 + 4 = 22 from the left. From the right end: 32 − 22 + 1 = 11.

APRS26-08-20 | Position via relative offset | Medium

21. C. Vikram is 10th from the left, i.e. position 10 from the left. 18 people between them means Pooja is 19 places to the right: 10 + 19 = 29 from the left. So Pooja's position from the left end is 29.

APRS26-08-21 | Position via relative offset | Medium

22. C. Total = (Rank from top) + (Rank from bottom) − 1 = 38 + 34 − 1 = 71.

APRS26-08-22 | Total from two ranks | Medium

23. A. New total = 41 + 6 = 47. Since the change is at the bottom, Kavita's rank from the top stays 12. Rank from bottom = 47 − 12 + 1 = 36.

APRS26-08-23 | Rank after a change | Medium

24. D. Rank from bottom = Total − Rank from top + 1 = 71 − 69 + 1 = 3.

APRS26-08-24 | Rank conversion | Medium

25. D. Total = (Rank from top) + (Rank from bottom) − 1 = 32 + 12 − 1 = 43.

APRS26-08-25 | Total from two ranks | Medium

26. D. Sanjay is 6th from the left, i.e. position 6 from the left. 15 people between them means Kavita is 16 places to the right: 6 + 16 = 22 from the left. So Kavita's position from the left end is 22.

APRS26-08-26 | Position via relative offset | Medium

27. D. Priya is 21st from the left, i.e. position 21 from the left. Facing north, "right" means towards the right end, so Anjali is at 21 + 12 = 33 from the left. So Anjali's position from the left end is 33.

APRS26-08-27 | Position via relative offset | Medium

28. C. Anjali is 17th from the right, so from the left Anjali is at 25 − 17 + 1 = 9. Facing north, "left" means towards the left end, so Aman is at 9 − 4 = 5 from the left. From the right end: 25 − 5 + 1 = 21.

APRS26-08-28 | Position via relative offset | Medium

29. B. Divya is 50th from the left, i.e. position 50 from the left. Facing north, "left" means towards the left end, so Priya is at 50 − 14 = 36 from the left. So Priya's position from the left end is 36.

APRS26-08-29 | Position via relative offset | Medium

30. D. Number of people strictly between the two ranks = |37 − 12| − 1 = 24.

APRS26-08-30 | People between two ranks | Medium

31. A. New total = 51 − 5 = 46. Since the change is at the top, Divya's rank from the top shifts to 20 − 5 = 15. Rank from bottom = 46 − 15 + 1 = 32.

APRS26-08-31 | Rank after a change | Medium

32. C. Number of people strictly between the two ranks = |47 − 19| − 1 = 27.

APRS26-08-32 | People between two ranks | Medium

33. C. New total = 55 + 4 = 59. Since the change is at the bottom, Kavita's rank from the top stays 37. Rank from bottom = 59 − 37 + 1 = 23.

APRS26-08-33 | Rank after a change | Medium

34. A. Total = (Rank from top) + (Rank from bottom) − 1 = 36 + 10 − 1 = 45.

APRS26-08-34 | Total from two ranks | Medium

35. B. New total = 39 + 6 = 45. Since the change is at the bottom, Divya's rank from the top stays 11. Rank from bottom = 45 − 11 + 1 = 35.

APRS26-08-35 | Rank after a change | Medium

36. D. Total = (Rank from top) + (Rank from bottom) − 1 = 14 + 35 − 1 = 48.

APRS26-08-36 | Total from two ranks | Medium

37. D. Divya is 19th from the left, i.e. position 19 from the left. 15 people between them means Neha is 16 places to the right: 19 + 16 = 35 from the left. So Neha's position from the left end is 35.

APRS26-08-37 | Position via relative offset | Medium

38. A. Total = (Rank from top) + (Rank from bottom) − 1 = 38 + 11 − 1 = 48.

APRS26-08-38 | Total from two ranks | Medium

39. B. Rank from bottom = Total − Rank from top + 1 = 64 − 45 + 1 = 20.

APRS26-08-39 | Rank conversion | Medium

40. B. Priya is 17th from the right, so from the left Priya is at 56 − 17 + 1 = 40. 12 people between them means Pooja is 13 places to the left: 40 − 13 = 27 from the left. From the right end: 56 − 27 + 1 = 30.

APRS26-08-40 | Position via relative offset | Medium

41. D. Number of people strictly between the two ranks = |46 − 10| − 1 = 35.

APRS26-08-41 | People between two ranks | Difficult

42. B. Total = (Rank from top) + (Rank from bottom) − 1 = 52 + 38 − 1 = 89.

APRS26-08-42 | Total from two ranks | Difficult

43. A. Number of people strictly between the two ranks = |29 − 11| − 1 = 17.

APRS26-08-43 | People between two ranks | Difficult

44. D. Karan is 54th from the left, i.e. position 54 from the left. Facing north, "right" means towards the right end, so Divya is at 54 + 12 = 66 from the left. So Divya's position from the left end is 66.

APRS26-08-44 | Position via relative offset | Difficult

45. B. Priya is 66th from the left, i.e. position 66 from the left. Facing north, "left" means towards the left end, so Neha is at 66 − 8 = 58 from the left. From the right end: 71 − 58 + 1 = 14.

APRS26-08-45 | Position via relative offset | Difficult

46. B. Total = (Rank from top) + (Rank from bottom) − 1 = 26 + 58 − 1 = 83.

APRS26-08-46 | Total from two ranks | Difficult

47. C. Karan is 10th from the right, so from the left Karan is at 48 − 10 + 1 = 39. Facing north, "left" means towards the left end, so Pooja is at 39 − 11 = 28 from the left. From the right end: 48 − 28 + 1 = 21.

APRS26-08-47 | Position via relative offset | Difficult

48. D. Divya is 67th from the left, i.e. position 67 from the left. 7 people between them means Neha is 8 places to the left: 67 − 8 = 59 from the left. From the right end: 77 − 59 + 1 = 19.

APRS26-08-48 | Position via relative offset | Difficult

49. B. New total = 63 + 6 = 69. Since the change is at the bottom, Sneha's rank from the top stays 44. Rank from bottom = 69 − 44 + 1 = 26.

APRS26-08-49 | Rank after a change | Difficult

50. A. Number of people strictly between the two ranks = |49 − 16| − 1 = 32.

APRS26-08-50 | People between two ranks | Difficult