The students in three classes are in the ratio 2 : 3 : 5. If 40 studen...
Understanding the problem
We are given that the students in three classes are in the ratio 2:3:5. We need to find the total number of students originally.
Solution
Let's assume the common ratio between the classes is 'x'. Therefore, the number of students in the three classes can be represented as 2x, 3x, and 5x respectively.
According to the problem, when 40 students are added to each class, the new ratio becomes 4:5:7. Therefore, the new number of students in the three classes can be represented as 2x + 40, 3x + 40, and 5x + 40 respectively.
Forming equations
We can form two equations based on the given information:
1) (2x + 40) : (3x + 40) : (5x + 40) = 4 : 5 : 7
2) (2x) : (3x) : (5x) = 2 : 3 : 5
Solving the equations
We can solve these equations to find the value of 'x'.
Equation 1:
(2x + 40) : (3x + 40) : (5x + 40) = 4 : 5 : 7
Simplifying the equation by cross-multiplication:
4(3x + 40) = 5(2x + 40)
12x + 160 = 10x + 200
12x - 10x = 200 - 160
2x = 40
x = 20
Equation 2:
(2x) : (3x) : (5x) = 2 : 3 : 5
Substituting the value of 'x' as 20:
(2 * 20) : (3 * 20) : (5 * 20) = 2 : 3 : 5
40 : 60 : 100 = 2 : 3 : 5
Calculating the total number of students
To find the original total number of students, we add the number of students in each class:
2x + 3x + 5x = 2(20) + 3(20) + 5(20) = 40 + 60 + 100 = 200
Therefore, the total number of students originally was 200.
The correct answer is option 'C' - 200.