The ratio of boys to girls in a class is 7 to 3. Among the options below, an acceptable value for the total number of students in the class is:
Ratio Understanding
The ratio of boys to girls is given as 7 to 3 (7:3). This means that for every group of students represented by this ratio, there are 7 parts boys and 3 parts girls.
Calculating Total Parts
The total number of parts in the ratio is the sum of the parts for boys and girls:
$ \text{Total Parts} = 7 (\text{boys}) + 3 (\text{girls}) = 10 \text{ parts} $
Determining Acceptable Total Students
The total number of students in the class must be divisible by the total number of parts (10). This ensures that the number of boys and girls are whole numbers, maintaining the 7:3 ratio.
We need to find which option is a multiple of 10:
- Option 1: 21 is not divisible by 10.
- Option 2: 37 is not divisible by 10.
- Option 3: 50 is divisible by 10 ($50 \div 10 = 5$).
- Option 4: 73 is not divisible by 10.
Therefore, 50 is the only acceptable value for the total number of students.
Important Questions from Ratio and Proportion
If the ratio of three numbers A, B and C is 2 ∶ 3 ∶ 5, and the sum of the squares of these numbers is 3800, then the value of C is:
A bag contains ₹310 in the form of 5 rupee, 2 rupee and 1 rupee coins in the ratio 4 ∶ 3 ∶ 5. What is the number of 5 rupee coins?
The ratio of three numbers is 3 ∶ 5 ∶ 4 and the sum of their squares is 11250. Find the sum of the numbers.
When 'x' is subtracted from each of the numbers 22, 39, 56 and 107, then the resulting numbers, in this order, are in proportion. What is the mean proportional between (x + 3) and (3x - 7)?
The salaries of Ravi and Sumit are in the ratio 4 ∶ 5. If the salary of each is increased by Rs. 6,000 the new ratio becomes 35 ∶ 40. What will be Sumit's increased salary?
