The number of students in three classes is in the ratio \(3:13:6\). If 18 students are added to each class, the ratio changes to \(15:35:21\).
The total number of students in all the three classes in the beginning was:
The total number of students in all the three classes in the beginning was:
Show Hint
- 22
- 66
- 88
- 110
The Correct Option is C
Solution and Explanation
Step 1: Assume the initial numbers of students.
Let the number of students in the three classes initially be
\[
3x,\; 13x,\; 6x.
\]
Step 2: Add 18 students to each class.
After adding 18 students to each class, the numbers become
\[
3x+18,\; 13x+18,\; 6x+18.
\]
Step 3: Use the new ratio.
According to the question,
\[
\frac{3x+18}{15} = \frac{13x+18}{35} = \frac{6x+18}{21}.
\]
Step 4: Solve using the first two terms.
\[
\frac{3x+18}{15} = \frac{13x+18}{35}
\]
\[
35(3x+18) = 15(13x+18)
\]
\[
105x + 630 = 195x + 270
\]
\[
360 = 90x $\Rightarrow$ x = 4.
\]
Step 5: Find the total number of students initially.
\[
3x + 13x + 6x = 22x = 22 \times 4 = 88.
\]
% Final Answer
Final Answer: \[ \boxed{88} \]
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