The number of students in three classes are in the ratio 1:3:5. If 60 students are increased in each class, the ratio changes to 3:5:7. Originally, the total number of students was :

Options

A. 180
B. 250
C. 270
D. none of there

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript.

### Step 1: Define the ratio
The number of students in three classes is given in the ratio 1:3:5. We can represent the number of students in each class as:
- Class 1: \( x = 1r \)
- Class 2: \( y = 3r \)
- Class 3: \( z = 5r \)

### Step 2: Set up the equation after increasing students
When 60 students are added to each class, the new number of students becomes:
- Class 1: \( x + 60 = 1r + 60 \)
- Class 2: \( y + 60 = 3r + 60 \)
- Class 3: \( z + 60 = 5r + 60 \)

The new ratio is given as 3:5:7. Thus, we can write the following equations based on the new ratio:
\[ \frac{1r + 60}{3} = \frac{3r + 60}{5} = \frac{5r + 60}{7} \]

### Step 3: Set up the first equation
We will set up the first equation using the first two parts of the new ratio:
\[ \frac{1r + 60}{3} = \frac{3r + 60}{5} \]
Cross-multiplying gives:
\[ 5(1r + 60) = 3(3r + 60) \]
Expanding both sides:
\[ 5r + 300 = 9r + 180 \]

### Step 4: Solve for \( r \)
Rearranging the equation:
\[ 300 - 180 = 9r - 5r \]
\[ 120 = 4r \]
\[ r = 30 \]

### Step 5: Calculate the original number of students
Now that we have \( r \), we can find the number of students in each class:
- Class 1: \( 1r = 1 \times 30 = 30 \)
- Class 2: \( 3r = 3 \times 30 = 90 \)
- Class 3: \( 5r = 5 \times 30 = 150 \)

### Step 6: Find the total number of students
Now, we can find the total number of students:
\[ \text{Total} = 30 + 90 + 150 = 270 \]

### Conclusion
The original total number of students was **270**.

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