Solving Rank Calculation Problems

This question involves calculating the number of students positioned between two individuals, Ravi and Raj, based on their ranks in a class. We are given the total number of students, Ravi's specific rank, and information to determine Raj's rank.

Understanding the Given Information

• Total students in the class: 45
• Ravi's rank from the top: 9th
• Number of students below Raj's rank: 18

Determining Ravi's Position

Ravi's rank is given as 9th from the top. This means there are 8 students ahead of Ravi.

Determining Raj's Rank

We are told that there are 18 students below Raj's rank. To find Raj's rank from the top, we subtract the number of students below him from the total number of students and add 1 (for Raj himself).

Raj's rank = (Total students) - (Students below Raj) + 1

Raj's rank = $45 - 18 + 1$

Raj's rank = $27 + 1$

Raj's rank = 28th from the top.

Let's re-read the information carefully: "There are 18 students below Raj Rankwise". This phrasing usually implies Raj's rank itself accounts for the position, and the count '18' refers strictly to those *behind* him. So, if 18 students are behind Raj, his position from the *top* is Total - (students behind) = $45 - 18 = 27$th.

Let's confirm: If Raj is 27th, there are $45 - 27 = 18$ students behind him. This aligns with the statement.

So, Raj's rank from the top is 27th.

Calculating Students Between Ravi and Raj

Now we have:

• Ravi's rank: 9th
• Raj's rank: 27th

To find the number of students strictly *between* them, we calculate the difference between their ranks and subtract 1 (because the difference includes one of the ranks themselves).

Number of students between Ravi and Raj = (Raj's Rank - Ravi's Rank) - 1

Number of students between = $(27 - 9) - 1$

Number of students between = $18 - 1$

Number of students between = $17$

Conclusion

Therefore, there are 17 students ranked between Ravi and Raj.