In a class `(3)/(5)` of the students are girls and rest are boys.If `(2)/(9)` of the girls and `(1)/(4)` of the boys are absent .What part of the total number of students are present?

Options

A. `(23)/(30)`
B. `(23)/(36)`
C. `(18)/(49)`
D. `(17)/(25)`

Answer

To solve the problem step-by-step, we will follow the logical deductions made in the video transcript.

### Step 1: Define the Total Number of Students
Let the total number of students in the class be represented by \( T \). According to the problem, \( \frac{3}{5} \) of the students are girls.

### Step 2: Calculate the Number of Girls and Boys
From the total number of students \( T \):
- Number of girls = \( \frac{3}{5} T \)
- Number of boys = \( T - \frac{3}{5} T = \frac{2}{5} T \)

### Step 3: Determine the Absent Girls
We know that \( \frac{2}{9} \) of the girls are absent. Therefore, the number of absent girls is:
\[ \text{Absent girls} = \frac{2}{9} \times \frac{3}{5} T = \frac{6}{45} T = \frac{2}{15} T \]

### Step 4: Calculate the Present Girls
The number of girls present can be calculated as:
\[ \text{Present girls} = \text{Total girls} - \text{Absent girls} = \frac{3}{5} T - \frac{2}{15} T \]
To subtract these fractions, we need a common denominator. The least common multiple of 5 and 15 is 15:
\[ \frac{3}{5} T = \frac{9}{15} T \]
Thus,
\[ \text{Present girls} = \frac{9}{15} T - \frac{2}{15} T = \frac{7}{15} T \]

### Step 5: Determine the Absent Boys
Next, we know that \( \frac{1}{4} \) of the boys are absent. Therefore, the number of absent boys is:
\[ \text{Absent boys} = \frac{1}{4} \times \frac{2}{5} T = \frac{2}{20} T = \frac{1}{10} T \]

### Step 6: Calculate the Present Boys
The number of boys present can be calculated as:
\[ \text{Present boys} = \text{Total boys} - \text{Absent boys} = \frac{2}{5} T - \frac{1}{10} T \]
Again, we need a common denominator. The least common multiple of 5 and 10 is 10:
\[ \frac{2}{5} T = \frac{4}{10} T \]
Thus,
\[ \text{Present boys} = \frac{4}{10} T - \frac{1}{10} T = \frac{3}{10} T \]

### Step 7: Calculate the Total Present Students
Now we can find the total number of students present:
\[ \text{Total present} = \text{Present girls} + \text{Present boys} = \frac{7}{15} T + \frac{3}{10} T \]
To add these fractions, we need a common denominator. The least common multiple of 15 and 10 is 30:
\[ \frac{7}{15} T = \frac{14}{30} T \quad \text{and} \quad \frac{3}{10} T = \frac{9}{30} T \]
Thus,
\[ \text{Total present} = \frac{14}{30} T + \frac{9}{30} T = \frac{23}{30} T \]

### Step 8: Find the Part of Total Students Present
Finally, the part of the total number of students that are present is:
\[ \text{Part of total students present} = \frac{\text{Total present}}{T} = \frac{\frac{23}{30} T}{T} = \frac{23}{30} \]

### Final Answer
The part of the total number of students that are present is \( \frac{23}{30} \).

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