Step-by-step Solution:

Quick Solution

The question asks for the greatest number of people who can ride, given the specific starting condition that Feroz and Harish both ride. We'll use this as our starting point and follow the chain of logical deductions from the rules.

1. Initial Deductions from the Starting Condition

If we begin with the fact that Feroz (F) and Harish (H) are riding:

• Rule 1 ("If Feroz rides Gautam must ride") is immediately triggered.
  
  ✔️ This means Gautam (G) must also ride.
  
• Now that we know both G and H are riding, Rule 2 ("If Gautam and Harish both ride, Javed cannot ride") is triggered.
  
  ❌ This means Javed (Jv) must NOT ride.
  

Current Status: Riding: {Feroz, Harish, Gautam}
Not Riding: {Javed}

2. Maximizing the Group from Remaining People

- The remaining friends to consider are {Kumar, Laxman, Mohan}.
- Since Javed is not riding, the rules that begin with "If Javed rides..." do not apply to our scenario.

The only rule left that affects these three is Rule 7: "Kumar and Mohan cannot both ride."

• This means to maximize our group, we can add at most one person from the pair {Kumar, Mohan}.
• There are no rules restricting Laxman, so we can add him to the group.

To get the greatest number of people, we will add Laxman and we will add one person from the {Kumar, Mohan} pair (let's say Kumar).

3. The Final Group and Answer

The largest possible group that satisfies all the conditions is:

{Feroz, Harish, Gautam, Laxman, Kumar}

The total number of people in this valid group is 5.

Final Answer: The greatest number of people who can ride is 5.