Rank Calculation Explained: John's Bottom Rank
This problem involves finding a student's position in a class when their rank from the top is known, along with the total number of students.
Understanding Ranking Positions
When we talk about ranks, we consider positions from both the top and the bottom of a group. If you know the total number of people and someone's position from one end (either top or bottom), you can easily find their position from the other end.
The Ranking Formula
The relationship between rank from the top, rank from the bottom, and the total number of students can be expressed with a simple formula. Let:
- \(N\) = Total number of students in the class
- \(R_{top}\) = Rank from the top
- \(R_{bottom}\) = Rank from the bottom
The formula is:
\(N = R_{top} + R_{bottom} - 1\)
To find the rank from the bottom (\(R_{bottom}\)), we can rearrange the formula:
\(R_{bottom} = N - R_{top} + 1\)
Applying the Formula to John's Rank
We are given the following information:
- Total number of students, \(N = 40\)
- John's rank from the top, \(R_{top} = 12\)
Now, we substitute these values into the formula to calculate John's rank from the bottom:
\(R_{bottom} = 40 - 12 + 1\)
Step-by-Step Calculation
- Start with the total number of students: \(40\).
- Subtract John's rank from the top: \(40 - 12 = 28\). This tells us there are 28 students ranked below John.
- Add 1 to include John himself in the count from the bottom. So, \(28 + 1 = 29\).
Therefore, John's rank from the bottom is \(29\).
Conclusion
John's rank from the bottom is \(29^{th}\). This means there are 28 students ranked below him in the class of 40 students.
Similar Questions
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Important Questions from Ordering and Ranking
A medical representative plans to visit each of six hospitals — A, B, C, D, E and F — exactly once during the course of one day. He is setting up his schedule for the day according to the following conditions:
i. He must visit A before B and E.
ii. He must visit B before D.
iii. The third hospital he visits must be C.
Which of the following could be the possible order in which the medical representative visits the six hospitals?Sonam is older than Renu. Komal is younger than Renu. Priya is older than Sonam. Who is the eldest of them?
Five men P, Q, R, S and T are reading a newspaper. The one who reads it first, gives it to T. The one who reads it last, had taken it from R. Q is not the first or last one to read it. There were two readers between P and R. Who is the third one to have read the newspaper?
P, Q, R, S, T and U are standing in a queue. Q is just ahead of P. S is just behind T. U is NOT near R, who is separated from Q by two persons. Who is standing at the front of the queue?
Five students took part in a cycling competition. Robert finished before Monish but behind Gunjan. Anil finished before Sunil but behind Monish.
Who won the competition?
