Question

the students in three classes are in ratio 2:3:5. if 40 are increased in each class, the ratio changes to 4:5:7. originally the total no. of students was?
(a) 100
(b)120
(c)200
(d)400
give solution to this question..​

Answer 1

Answer:

Total students are 200

Step-by-step explanation:

Given the ratio of students in three classes = 2 : 3 : 5

Let the student in class 1 $= 2x$

Let the student in class 2 $= 3x$

Let the student in class 3 $= 5x$

Given that 40 students are increased in each class, ratio is changed to 4 : 5 : 7

Student in class 1 $= 2x + 40$

Student in class 2 $= 3x + 40$

Student in class 3 $= 5x + 50$

Thus, we get

$\frac{2x + 40}{3x + 40} = \frac{4}{5}\\\\ 5 \times (\,2x + 40)\, = 4 \times (\,3x + 40)\,\\\\10x + 200 = 12x + 160\\\\ 12x - 10x = 200 - 160\\\\2x = 40\\\\ x = 20$

Thus,

Student is Class 1 $= 2 \times 20 = 40$

Student is Class 2 $= 3 \times 20 = 60$

Student is Class 3 $= 5 \times 20 = 100$

Thus, total students = 40 + 60 + 100 = 200