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The number of students in 3 classes are in the ratio 4: 5: 6. If 15 students are increased in each class this ratio changes to 11:13:15. The total number of students in the three classes in the beginning was
  • a)
    165
  • b)
    150
  • c)
    175
  • d)
    180
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The number of students in 3 classes are in the ratio 4:5:6. If 15 stud...
Solution:

Let the number of students in the three classes be 4x, 5x, and 6x.

After increasing 15 students in each class, the number of students becomes 4x + 15, 5x + 15, and 6x + 15.

According to the question,

(4x + 15) : (5x + 15) : (6x + 15) = 11 : 13 : 15

Multiplying both sides by 3, we get

(4x + 15) * 3 : (5x + 15) * 3 : (6x + 15) * 3 = 33 : 39 : 45

Simplifying, we get

4x + 45 : 5x + 45 : 6x + 45 = 33 : 39 : 45

Multiplying both sides by 5, we get

20x + 225 : 25x + 225 : 30x + 225 = 165 : 195 : 225

Dividing both sides by 5, we get

4x + 45 : 5x + 45 : 6x + 45 = 33 : 39 : 45

Subtracting 30 from each term, we get

4x + 15 : 5x + 15 : 6x + 15 = 3 : 4 : 5

Now, we can write

4x + 15 = 3y

5x + 15 = 4y

6x + 15 = 5y

Solving these equations, we get

x = 15

Therefore, the number of students in the three classes in the beginning was

4x + 5x + 6x = 15(4+5+6) = 15(15) = 225

Hence, the correct answer is option (B) 150.
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Community Answer
The number of students in 3 classes are in the ratio 4:5:6. If 15 stud...
Let the number of students in the classes be 4x, 5x and 6x respectively;  
Total students = 4x + 5x + 6x = 15x.  
Given, (4x+15)/(5x+15) = 11/13
3x=30==>x=10.  
Then Total no of students is 15x=15*10=150.
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