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The students in three classes are in the ratio 4 : 6 : 9. If 12 students are increased in each class, the ratio changes to 7 : 9 : 12. Then the total number of students in the 2nd Class before the increase is
  • a)
    36
  • b)
    24
  • c)
    54
  • d)
    30
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The students in three classes are in the ratio 4 : 6 : 9. If 12 studen...
The Initial ratio is 4 : 6 : 9
Let the common ratio be ‘x’
Therefore the respective number of students in the 3 classes will be 4x , 6x and 9x
After addition of 12 students to each class,
The numbers will be 4x + 12 , 6x + 12, 9x + 12
The ratio after that will be 7 : 9 : 12
∴ (4x + 12)/(6x + 12) = 7/9
∴ 9 × (4x + 12) = 7 × (6x + 12)
∴ 36x + 108 = 42x + 84
∴ 6x = 24
∴ x = 4
∴ The initial number of students in the 2nd class = 24
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Most Upvoted Answer
The students in three classes are in the ratio 4 : 6 : 9. If 12 studen...
Given:
The ratio of students in three classes is 4:6:9.

To find:
The total number of students in the 2nd Class before the increase.

Solution:
Let's assume the initial number of students in the three classes as 4x, 6x, and 9x respectively.

After increasing 12 students in each class, the new ratio becomes 7:9:12.

Step 1:
Write the equation based on the given information:

(4x + 12) : (6x + 12) : (9x + 12) = 7 : 9 : 12

Step 2:
Since the ratio is in proportion, we can cross multiply:

(4x + 12) * 12 = (6x + 12) * 7
(6x + 12) * 9 = (9x + 12) * 7

Step 3:
Solve the equations to find the value of x:

48x + 144 = 84x + 84
54x + 108 = 63x + 84

Simplifying the equations further:

36x = 60
9x = 24

Step 4:
Find the total number of students in the 2nd class before the increase:

Number of students in the 2nd class = 6x
= 6 * 24
= 144

Therefore, the total number of students in the 2nd class before the increase is 144 (Option B).
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The students in three classes are in the ratio 4 : 6 : 9. If 12 students are increased in each class, the ratio changes to 7 : 9 : 12. Then the total number of students in the 2nd Class before the increase isa)36b)24c)54d)30Correct answer is option 'B'. Can you explain this answer?
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