Understanding the Class Ranking Problem
This problem involves calculating the number of boys behind a specific student (Rohan) in a class, considering the total number of students, the ratio of boys to girls, and Rohan's rank from the top, along with the number of girls ahead of him.
Step 1: Calculate the Total Number of Boys and Girls
We are given:
- Total students in the class = 120
- Number of boys is twice the number of girls.
Let '$G$' be the number of girls and '$B$' be the number of boys.
From the given information, we can set up the following equations:
- \(B + G = 120\)
- \(B = 2G\)
Now, substitute the second equation into the first:
\((2G) + G = 120\)
\(3G = 120\)
\(G = \frac{120}{3}\)
\(G = 40\)
So, there are 40 girls in the class.
Now, calculate the number of boys:
\(B = 2G = 2 \times 40 = 80\)
Therefore, there are 80 boys in the class.
Step 2: Determine the Number of Students Ahead of Rohan
Rohan is ranked 28th from the top. This means there are 27 students ahead of him.
Total students ahead of Rohan = Rank - 1
Total students ahead of Rohan = \(28 - 1 = 27\)
Step 3: Calculate the Number of Boys Ahead of Rohan
We know that out of the 27 students ahead of Rohan:
- Number of girls ahead of Rohan = 18
To find the number of boys ahead of Rohan, subtract the number of girls ahead from the total students ahead:
Number of boys ahead of Rohan = (Total students ahead of Rohan) - (Number of girls ahead of Rohan)
Number of boys ahead of Rohan = \(27 - 18 = 9\)
So, there are 9 boys ahead of Rohan.
Step 4: Calculate the Number of Boys Behind Rohan
We need to find the number of boys behind Rohan. Assuming Rohan is a boy (as the question asks for the number of *boys* behind him, implying his inclusion or exclusion is relevant to the count of boys):
- Total number of boys in the class = 80
- Number of boys ahead of Rohan = 9
The number of boys behind Rohan is the total number of boys minus the boys ahead of him and Rohan himself.
Number of boys behind Rohan = (Total boys) - (Boys ahead of Rohan) - 1 (Rohan)
Number of boys behind Rohan = \(80 - 9 - 1 = 70\)
Final Answer Calculation Summary
| Category | Count |
|---|---|
| Total Students | 120 |
| Total Girls (G) | 40 |
| Total Boys (B) | 80 |
| Rohan's Rank (from top) | 28 |
| Students Ahead of Rohan | 27 |
| Girls Ahead of Rohan | 18 |
| Boys Ahead of Rohan | 9 |
| Boys Behind Rohan | 70 |
Therefore, there are 70 boys behind Rohan.
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?
