This problem involves logical deduction to determine the schedule of 8 people (Paro, Runa, Sona, Kim, Harry, Ram, Geet, Monu) going on holiday during 8 different months (January to August). We need to find the number of people scheduled between Geet and Runa.

1. Analyzing Month Constraints

First, let's list the months and their number of days, identifying which have an odd or even number of days. This is crucial for placing Sona, Runa, and Ram.

2. Step-by-Step Deduction of Schedule

Let's use the given clues to build the schedule step-by-step:

• Clue 1: Harry goes in August.
  • August: Harry
• Clue 2: Sona goes in a month with an odd number of days.
  • Possible months for Sona: January, March, May, July, August.
  • Since Harry is in August, Sona can be in January, March, May, or July.
• Clue 3: Geet goes just after the month in which Sona goes.
  • If Sona=Jan, Geet=Feb.
  • If Sona=Mar, Geet=Apr.
  • If Sona=May, Geet=Jun.
  • If Sona=Jul, Geet=Aug. (This is impossible because Harry is in August).
  • Therefore, the possible pairs for (Sona, Geet) are (Jan, Feb), (Mar, Apr), or (May, Jun).
• Clue 5 & 7: Runa goes in an even number of days month (not Feb). Ram does not go in odd days month (so even days) and not in Feb.
  • Possible even months: February, April, June, August.
  • Runa cannot go in February. Harry is in August. So, Runa must go in April or June.
  • Ram also cannot go in February or odd months. Harry is in August. So, Ram must go in April or June.
  • This means Runa and Ram occupy the months of April and June between them.
• Testing the Possible (Sona, Geet) Pairs:
  • Case A: (Sona=Jan, Geet=Feb)
    • Current Schedule: Sona=Jan, Geet=Feb, Harry=Aug.
    • Runa and Ram must be in Apr and Jun.
    • Clue 4: Three persons go between Monu and Sona. Since Sona is in Jan (1st month), Monu must be in the 5th month (Jan + 3 people + 1 position = 5th month), which is May. (Monu=May)
    • Current Schedule: Sona=Jan, Geet=Feb, Monu=May, Harry=Aug. Runa/Ram in Apr/Jun. Remaining months: Mar, Jul. Remaining people: Kim, Paro.
    • Clue 6: Two persons go between Kim and Ram. Ram must be in Apr or Jun.
      • If Ram=Apr: Kim must be 2 months before (impossible) or 2 months after. 2 months after Apr is Jun (taken by Runa) or Aug (taken by Harry). Wait, let's check month positions. Ram=Apr(4). 2 people between Kim and Ram means Kim=Month 1 or Month 7. Kim cannot be Jan (Sona). So Kim=Jul(7).
      • If Ram=Jun: Kim must be 2 months before, which is Apr (taken by Runa) or 2 months after (impossible). So, if Ram=Jun, Kim cannot be placed 2 months apart. Let's recheck Kim/Ram. Ram in Apr(4). Kim could be 4-3=1 (Jan, Sona) or 4+3=7 (Jul). Kim must be Jul(7). Runa must be Jun(6).
    • Let's assume Ram=Apr(4) and Runa=Jun(6). Then Kim must be Jul(7). The remaining person Paro must be in the remaining month Mar(3).
      • Tentative Schedule: Jan:Sona, Feb:Geet, Mar:Paro, Apr:Ram, May:Monu, Jun:Runa, Jul:Kim, Aug:Harry.
      • Clue 9: Paro does not go after Kim. Here, Paro is in Mar and Kim is in Jul. Paro goes before Kim. This condition is satisfied.
      • This schedule seems valid. Let's check the number of people between Geet and Runa. Geet is in Feb (2nd month), Runa is in Jun (6th month). People between them are in Mar, Apr, May (Paro, Ram, Monu). There are 3 people.
    • Now consider the other possibility: Ram=Jun(6) and Runa=Apr(4). Kim must be 2 months before or after Ram(Jun). 2 months before Jun is Apr (taken by Runa). 2 months after Jun is Aug (taken by Harry). This placement for Kim seems impossible if Ram=Jun. Let's re-read clue 6. Maybe it's about the people in between, not just months. "Two persons goes between Kim and Ram". If Ram is in June(6), Kim could be in March(3) (2 people Mar, Apr between them) or July(7) (1 person Jul between them, not valid) or Feb(2) (1 person Feb between them, not valid) or Jan(1) (2 people Jan, Feb between them). Let's check Kim=Mar(3).
      • Tentative Schedule: Sona=Jan, Geet=Feb, Kim=Mar, Runa=Apr, Monu=May, Ram=Jun, Harry=Aug.
      • Remaining month: Jul. Remaining person: Paro. Paro=Jul(7).
      • Check Clue 9: Paro (Jul) does not go after Kim (Mar). This is FALSE, Paro goes after Kim. So this sub-case is invalid.
    • The only valid setup derived from Case A is: Jan:Sona, Feb:Geet, Mar:Paro, Apr:Ram, May:Monu, Jun:Runa, Jul:Kim, Aug:Harry.
  • Case B: (Sona=Mar, Geet=Apr)
    • Current Schedule: Sona=Mar, Geet=Apr, Harry=Aug.
    • Runa and Ram must be in the remaining even months: June and August. But Harry is in August. So Runa and Ram must both be in June. This is impossible as they are different people. Case B is invalid.
  • Case C: (Sona=May, Geet=Jun)
    • Current Schedule: Sona=May, Geet=Jun, Harry=Aug.
    • Runa and Ram must be in the remaining even months: April and August. But Harry is in August. So Runa and Ram must both be in April. This is impossible. Case C is invalid.
• Conclusion: The only possible schedule derived is from Case A.

3. Final Determined Schedule

Based on the deductions, the final schedule is:

4. Calculating People Between Geet and Runa

Now, we need to find how many persons go between Geet and Runa.

• Geet is scheduled in February (Position 2).
• Runa is scheduled in June (Position 6).
• The persons scheduled in the months between February and June are those in March, April, and May.
• These persons are Paro (March), Ram (April), and Monu (May).
• Counting these individuals, there are 3 persons between Geet and Runa.

Therefore, 3 persons go between Geet and Runa.