Question : The students in three classes are in a ratio of 3 : 7 : 8. If 6 students are increased in each class, the ratio changes to 11 : 23 : 26. Find the total number of students in the three classes before the increase.
Option 1: 162
Option 2: 112
Option 3: 90
Option 4: 144
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Correct Answer: 162
Solution :
Initial ratio = $3: 7: 8$
Let the number of students in three classes be $3x, 7x$, and $8x$ respectively.
Increase in each class = 6
Number of students in three classes after the increase = $3x+6, 7x+6 $, and $8x+6$
Final ratio = $11:23:26$
$3x+6 : 7x+6 : 8x+6 = 11:23:26$
⇒ $\frac{3x+6}{7x+6} = \frac{11}{23}$
⇒ $(3x+6)×23 = (7x+6)×11$
⇒ $69x+138 = 77x+66 $
⇒ $8x = 72$
⇒ $x=9$
Total number of students initially = $3x+7x+8x$
$= 18x$
$= 18×9$
$= 162$
Hence, the correct answer is 162.
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