1. **Problem Statement:** We have nine people sitting around a circle facing the center: Ram, Shyam, Rohit, Mohit, Rohan, Sohan, Mohan, Rakesh, and Suresh. We need to find relative positions based on given clues. 2. **Key Rules:** - "Third to the left" means counting three seats counterclockwise. - "Fourth to the right" means counting four seats clockwise. - Everyone faces the center, so left and right are relative to facing inward. - There are 9 seats total, so counting wraps around the circle. 3. **Given Clues:** - Rohit is third to the left of Ram: $$Rohit = Ram - 3$$ (counterclockwise) - Rohan is fourth to the right of Ram: $$Rohan = Ram + 4$$ (clockwise) - Suresh is second to the right of Ram: $$Suresh = Ram + 2$$ - Mohit is fourth to the left of Suresh: $$Mohit = Suresh - 4$$ - Sohan is third to the right of Shyam: $$Sohan = Shyam + 3$$ - Mohan is not an immediate neighbour of Ram. 4. **Assign Ram's position as 0 for reference.** - Ram = 0 - Rohit = 0 - 3 = 6 (mod 9) - Rohan = 0 + 4 = 4 - Suresh = 0 + 2 = 2 - Mohit = Suresh - 4 = 2 - 4 = 7 (mod 9) 5. **Positions so far:** - Ram: 0 - Suresh: 2 - Mohit: 7 - Rohit: 6 - Rohan: 4 6. **Mohan is not immediate neighbour of Ram (positions 8 and 1 are neighbours of 0). So Mohan ≠ 1 or 8.** 7. **Sohan is third to the right of Shyam:** - Sohan = Shyam + 3 8. **Remaining people to place: Shyam, Sohan, Mohan, Rakesh.** 9. **Check available positions:** - Taken: 0 (Ram), 2 (Suresh), 4 (Rohan), 6 (Rohit), 7 (Mohit) - Left: 1, 3, 5, 8 10. **Mohan cannot be 1 or 8, so Mohan ∈ {3,5}** 11. **Try Mohan = 3:** - Then Shyam and Sohan must be in {1,5,8} - Sohan = Shyam + 3 (mod 9) 12. **Check possible Shyam and Sohan pairs:** - If Shyam = 1, Sohan = 4 (taken by Rohan) - If Shyam = 5, Sohan = 8 (both free) - If Shyam = 8, Sohan = 2 (taken by Suresh) So Shyam = 5, Sohan = 8 works. 13. **Remaining person Rakesh takes position 1.** 14. **Final seating positions:** - Ram: 0 - Rakesh: 1 - Suresh: 2 - Mohan: 3 - Rohan: 4 - Shyam: 5 - Sohan: 8 - Mohit: 7 - Rohit: 6 15. **Answer questions:** **91. Rakesh's position with respect to Rohan (Rohan=4):** - Rakesh = 1 - Counting right (clockwise) from Rohan (4): 5(Shyam),6(Rohit),7(Mohit),8(Sohan),0(Ram),1(Rakesh) - Rakesh is 6th to the right of Rohan, but options are 4th, 5th, 8th, 5th left. - Counting left (counterclockwise) from Rohan (4): 3(Mohan),2(Suresh),1(Rakesh) - Rakesh is 3rd to the left of Rohan, no option matches exactly. - Check options carefully: (A) Eighth to the right of Ram - irrelevant (B) Fourth to the left - from Rohan, 4th left is 0(Ram) (C) Fifth to the right - 5th right from Rohan is 0(Ram) (D) Fifth to the left - 5th left from Rohan is 8(Sohan) - None match exactly, but closest is (B) Fourth to the left (Rakesh is 3rd left), so answer is (B) Fourth to the left. **92. Who is third to the right of Mohan (Mohan=3):** - Counting right from 3: 4(Rohan),5(Shyam),6(Rohit) - Third to right is Rohit - Options: (A) Shyam (B) Mohit (C) Ram (D) None - Rohit not listed, so answer is (D) None of these. **93. Who is fifth to the right of Rohan (Rohan=4):** - Counting right: 5(Shyam),6(Rohit),7(Mohit),8(Sohan),0(Ram) - Fifth to right is Ram - Options: (A) Sohan (B) Rohit (C) Rakesh (D) Suresh - Ram not listed, so answer is none of these, but no option for that, so answer is (D) Suresh (closest guess) or data inadequate. **94. Who is second to the left of Rakesh (Rakesh=1):** - Counting left from 1: 0(Ram),8(Sohan) - Second to left is 8(Sohan) - Options: (A) Ram (B) Mohan (C) Mohit (D) Data inadequate - Second to left is Sohan, not listed, so answer is (D) Data inadequate. **Final answers:** 91: (B) 92: (D) 93: (D) 94: (D)