In a class of 36 students, the number of boys are twice the number of girls. In the class, there are 13 boys before Reema (girl) whose position is 19th in the class. How many girls are there in the class after Reema?
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Solving the Class Ranking Problem to Find Girls After Reema
This problem involves calculating the number of girls after a specific student (Reema) in a class, based on the total number of students, the ratio of boys to girls, and ranking information.
Step 1: Determine the Total Number of Boys and Girls in the Class
We are given the total number of students in the class and the relationship between the number of boys and girls.
- Total students = 36
- Number of boys = Twice the number of girls
Let ‘G’ be the number of girls and ‘B’ be the number of boys.
We have two equations based on the information:
- \(G + B = 36\)
- \(B = 2G\)
Substitute the second equation into the first one:
\(G + (2G) = 36\)
\(3G = 36\)
Now, solve for G:
\(G = \frac{36}{3}\)
\(G = 12\)
So, the total number of girls in the class is 12.
Now, find the number of boys using \(B = 2G\):
\(B = 2 \times 12\)
\(B = 24\)
Total students = Girls + Boys = \(12 + 24 = 36\). This matches the given total, confirming our calculation is correct.
| Category | Number |
|---|---|
| Total Students | 36 |
| Total Girls | 12 |
| Total Boys | 24 |
Step 2: Analyze Reema's Position and Students Before Her
Reema is a girl and her position in the class ranking is 19th.
- Reema's rank = 19th
- This means there are \(19 - 1 = 18\) students before Reema.
We are also told that there are 13 boys before Reema.
- Students before Reema = 18
- Boys before Reema = 13
The students before Reema consist of some boys and some girls.
Number of girls before Reema = (Total students before Reema) - (Number of boys before Reema)
Girls before Reema = \(18 - 13 = 5\)
| Category | Number |
|---|---|
| Total Students Before Reema | 18 |
| Boys Before Reema | 13 |
| Girls Before Reema | 5 |
Step 3: Calculate the Total Number of Girls Up to Reema's Position
To find the number of girls up to Reema's 19th position, we include the girls before her and Reema herself (since she is a girl).
- Girls before Reema = 5
- Reema = 1 (She is one girl)
Total number of girls up to Reema's position = (Girls before Reema) + (Reema)
Total girls up to 19th position = \(5 + 1 = 6\)
So, there are 6 girls in the class from rank 1 up to rank 19 (including Reema).
Step 4: Calculate the Number of Girls After Reema
We know the total number of girls in the class and the number of girls up to Reema's position. To find the girls after Reema, we subtract the girls up to Reema from the total number of girls.
- Total girls in the class = 12
- Total girls up to Reema's position = 6
Number of girls after Reema = (Total girls in the class) - (Total girls up to Reema's position)
Number of girls after Reema = \(12 - 6 = 6\)
Therefore, there are 6 girls in the class after Reema.
Summary of Calculations
- Total students = 36
- Ratio: Boys = 2 * Girls
- Total Girls = 12
- Total Boys = 24
- Reema's Rank = 19
- Students before Reema = 18
- Boys before Reema = 13
- Girls before Reema = \(18 - 13 = 5\)
- Girls up to Reema (including Reema) = \(5 + 1 = 6\)
- Girls after Reema = \(12 - 6 = 6\)
The final answer is 6.
Revision Table: Key Concepts
| Concept | Explanation |
|---|---|
| Total Students Calculation | Using ratios or given relationships to find the total number of different categories (boys/girls) in the class. |
| Ranking Analysis | Understanding that the rank indicates the position in a sequence and how many individuals are before that position. |
| Students Before a Rank | If someone is at rank 'n', there are 'n-1' students before them. |
| Calculating Subgroup Members Before a Rank | Subtracting known members of one subgroup (e.g., boys) from the total number of individuals before a rank to find the members of another subgroup (e.g., girls) before that rank. |
| Calculating Members After a Rank | Subtracting the number of members of a subgroup up to and including a certain rank from the total number of members of that subgroup. |
Additional Information on Class Ranking Problems
Class ranking problems are common in aptitude tests and involve understanding positions in a sequence. They often require you to deduce information about the composition of the group (like number of boys and girls) and then use ranking details to find specific counts before or after a given position.
- Always start by figuring out the total number of individuals in each category if not directly given.
- Pay close attention to whether the question asks about students 'before', 'after', 'up to', or 'at' a particular rank.
- Remember that the person at a specific rank is included when counting 'up to' that rank, but not when counting 'before' that rank.
- Break down the problem into smaller steps: find totals, then find counts before the rank, then find counts up to the rank, and finally find counts after the rank.
- If ranks are given from both ends (e.g., from the top and bottom), use the formula: Total students = (Rank from top) + (Rank from bottom) - 1.
These problems test your ability to read carefully, set up simple equations, and perform logical deductions based on the given constraints.
Important Questions from Rank Based
All 32 students in a class are standing in a row facing north. Akash is 12th from the right end while Priya is 18th from the left end. How many people are standing between Akash and Priya?
In a row of 21 children facing North, Nitin is third to the right of Sita who is ninth from the right end of the row. What is Nitin's position from the left end?
Selvam is on 9th position from upwards and on 38th position from downwards in a class. How many students are in class?
Six students, Abhay, Bhanu, Charu, David, Ekta and Farheen, are the top six rank holders in a school. The rank of Bhanu is between the ranks of Charu and David. Bhanu is on the fourth rank. There are two students between the ranks of Ekta and David. Ekta is at the lowest rank among all the given students. The rank of Abhay is immediately below the rank of Farheen. Who is on the fifth rank?
In a row of 35 students, Ramesh is at the 24th position from the beginning. The last two students left. What is Ramesh's position from the end of the row?
