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# The number of students in 3 classes is in the ratio 2 : 3 : 4. If 12 students are increased in each class this ratio changes to 8 : 11 : 14. The total number of students in the three classes in the beginning was

A. 162

B. 108

C. 96

D. 54

### Solution(By Examveda Team)

Let the number of students in the classes be 2x, 3x and 4x respectively;
Total students = 2x + 3x + 4x = 9x
\eqalign{ & {\text{According}}\,{\text{to}}\,{\text{the}}\,{\text{question}}, \cr & \frac{{ {2x + 12} }}{{ {3x + 12} }} = \frac{8}{{11}} \cr & or,\,24x + 96 = 22x + 132 \cr & or,\,2x = 132 - 96 \cr & or,\,x = \frac{{36}}{2} = 18 \cr & {\text{Hence,}} \cr & {\text{Original}}\,{\text{number}}\,{\text{of}}\,{\text{students}}, \cr & 9x = 9 \times 18 \cr & \,\,\,\,\,\,\,\, = 162 \cr}

This Question Belongs to Arithmetic Ability >> Ratio

1. Easy Method
Let's denote the initial number of students in the three classes as ( 2x ), ( 3x ), and ( 4x ).
After increasing each class by 12 students, the numbers become
( 2x + 12 ), ( 3x + 12 ), and ( 4x + 12 ).
We are given that these numbers are in the ratio
( 8 : 11 : 14 ).
Therefore, we can set up the following proportion equations:
[ frac{2x + 12}{8} = frac{3x + 12}{11} = frac{4x + 12}{14} ]
Let's equate the first and second fractions:
[ frac{2x + 12}{8} = frac{3x + 12}{11} ]
Cross-multiplying to solve for ( x ):
[ 11(2x + 12) = 8(3x + 12) ]
[ 22x + 132 = 24x + 96 ]
[ 132 - 96 = 24x - 22x ]
[ 36 = 2x ]
[ x = 18 ]
Next, let's equate the second and third fractions to confirm:
[ frac{3x + 12}{11} = frac{4x + 12}{14} ]
Cross-multiplying to solve for ( x ):
[ 14(3x + 12) = 11(4x + 12) ]
[ 42x + 168 = 44x + 132 ]
[ 168 - 132 = 44x - 42x ]
[ 36 = 2x ]
[ x = 18 ]
Both calculations for ( x ) are consistent. Therefore, the initial number of students in each class is:
[ 2x = 2(18) = 36 ]
[ 3x = 3(18) = 54 ]
[ 4x = 4(18) = 72 ]
The total number of students in the three classes initially is:
[ 36 + 54 + 72 = 162 ]
Option A: 162

2. Wow

3. Easy guys take two ratio
2 : 3
+12 +12
8 : 11
Cross multi and sub
8×3-11×2 = 11×12-8×12
2=36
1=18
Total origina sum 9×18 =162

4. where is 4+12??

5. Why we not consider 14?

6. ye kese hoa ...??
24x+96 = 22x+132
Or, 2x = 132-96
Or, x = 36/2 = 18
Hence, Original number of students,
9x = 9*18 = 162.

7. Any essy mathed.. Its very hard

8. Cross-multiplication has been done.
(2x+12)/(3x+12) = 8/11
11*(2x+12) = 8 *(3x+12)
24x+96 = 22x+132

9. i didn't understand from where it comes 24x+96 = 22x+132

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