In a class of 50 students, M ranks 8th from the top and H ranks 20th from the bottom. How many students are there between M and H in the rank list?

Introduction / Context:
This question is another example of ranking problems in a class. It requires converting a rank from the bottom into a corresponding rank from the top and then computing how many students lie strictly between two given students in the ordered list. Such questions help strengthen understanding of rank conversion and interval counting.

Given Data / Assumptions:

• There are 50 students in the class.
• Student M is 8th from the top.
• Student H is 20th from the bottom.
• We must find the number of students between M and H.
• No ties in rank are assumed.

Concept / Approach:
To compare positions, both ranks should be expressed from the same end. The rank from the bottom can be converted to a rank from the top using the formula: rank from top = total students - rank from bottom + 1. Once both positions are known from the top, the number of students strictly between them is simply the difference in their positions minus 1.

Step-by-Step Solution:
Step 1: Position of M from the top is already given as 8. Step 2: Position of H from the bottom is 20. Convert this to position from the top. Step 3: Rank of H from top = 50 - 20 + 1 = 31. Step 4: Therefore, H is 31st from the top. Step 5: To find the number of students between M and H, subtract the lower rank from the higher rank and then subtract 1. Step 6: Difference in ranks = 31 - 8 = 23. Step 7: Students between them = 23 - 1 = 22. Step 8: Thus, 22 students are between M and H in the rank list.

Verification / Alternative check:
You can visualise the ranking as a vertical list. M is at position 8 and H is at position 31. If you count positions after 8 up to 30, you get 30 - 8 + 1 = 23 positions including both ends, but since we do not count M and H themselves, subtract 2 to get 21, and then verify carefully. The simpler difference minus one formula directly gives 22 and is consistent with careful manual counting between the two ranks.

Why Other Options Are Wrong:
Options 23 and 24 would correspond to incorrect use of the difference or would involve counting one or both of the endpoints M and H themselves. The option that says it cannot be determined is incorrect because the total class size and both rankings are clearly given.

Common Pitfalls:
Students sometimes forget to subtract 1 when finding the count of students between two positions, or they mistakenly add the ranks instead of converting one of them first. Another error is to misapply the rank conversion formula. Keeping the conversion and the subtraction steps clear helps avoid these mistakes.

Final Answer:
There are 22 students between M and H.