Ratio Calculation: Finding the Number of Boys
The problem requires finding the number of boys in a school given the total number of students and the ratio of boys to girls.
1. Determine Total Ratio Parts
The ratio of boys to girls is given as 17 : 11. To find the total number of parts in the ratio, we add the parts representing boys and girls.
Total parts = Boys' parts + Girls' parts
$ \text{Total parts} = 17 + 11 = 28 $
2. Calculate the Value of One Ratio Part
The total number of students is 9,632. This total represents the 28 parts of the ratio. To find the value of one part, we divide the total number of students by the total number of parts.
Value of 1 part = Total Students / Total Parts
$ \text{Value of 1 part} = \frac{9,632}{28} $
$ \text{Value of 1 part} = 344 $
3. Calculate the Number of Boys
The number of boys corresponds to 17 parts of the ratio. To find the total number of boys, we multiply the value of one part by the number of parts representing boys.
Number of Boys = Value of 1 part $ \times $ Boys' parts
$ \text{Number of Boys} = 344 \times 17 $
$ \text{Number of Boys} = 5,848 $
Therefore, there are 5,848 boys in the school.
Important Questions from Ratio and proportion
A’s marks in Mathematics are directly proportional to practice time. In 6 hours of practice, A gets 70 marks. What should be the practice time (approximately) to get 90 marks?
The average of the areas of 2 similar triangles is 706.5 m2 whose perimeters are in the ratio of 6 : 11. What is 20% of the difference (in m2) in areas of both triangles?
In a triangle ABC, D and E are two points on sides AB and AC, respectively, such that DE is parallel to BC and AD : DB = 3 : 5. If AC = 5.6 cm, then find the value (in cm) of AE.
In a triangle ABC, P and Q are two points on AB and AC, respectively, such that PQ is parallel to BC. If AC = 5QC, then the ratio PQ : BC is equal to:
Find the mean proportional between 25 and 81.
