In a school there are 1800 students. Last day except 4% of the boys all the students were present in the school. Today except 5% of the girls all the students are present in the school, but in both the days no. of students present in the school, were same. The no. of girls in the school is :

Options

A. 1200
B. 800
C. 1000
D. 600

Answer

To solve the problem step by step, we will use the information given in the question to set up equations and find the number of girls in the school.

### Step 1: Define Variables
Let:
- \( B \) = number of boys in the school
- \( G \) = number of girls in the school

From the problem, we know that:
\[ B + G = 1800 \]

**Hint:** Start by defining the variables that represent the quantities you need to find.

### Step 2: Calculate Present Students Last Day
Last day, except for 4% of the boys, all students were present. This means that 96% of the boys were present. The number of students present last day can be calculated as:
\[ \text{Present last day} = G + (96\% \text{ of } B) = G + \frac{96}{100}B \]

**Hint:** Remember to convert the percentage to a decimal when calculating the number of students present.

### Step 3: Calculate Present Students Today
Today, except for 5% of the girls, all students were present. This means that 95% of the girls were present. The number of students present today can be calculated as:
\[ \text{Present today} = B + (95\% \text{ of } G) = B + \frac{95}{100}G \]

**Hint:** Again, convert the percentage to a decimal to find the number of students present.

### Step 4: Set Up the Equation
According to the problem, the number of students present last day is equal to the number of students present today:
\[ G + \frac{96}{100}B = B + \frac{95}{100}G \]

**Hint:** This equation is key to solving for the number of girls and boys.

### Step 5: Rearrange the Equation
Rearranging the equation gives:
\[ G - \frac{95}{100}G = B - \frac{96}{100}B \]
This simplifies to:
\[ \frac{5}{100}G = \frac{4}{100}B \]
Multiplying through by 100 to eliminate the fraction:
\[ 5G = 4B \]

**Hint:** Isolate one variable to express it in terms of the other.

### Step 6: Express \( G \) in Terms of \( B \)
From the equation \( 5G = 4B \), we can express \( G \) as:
\[ G = \frac{4}{5}B \]

**Hint:** This relationship will help us substitute values in the next steps.

### Step 7: Substitute into the Total Students Equation
Substituting \( G \) into the total students equation \( B + G = 1800 \):
\[ B + \frac{4}{5}B = 1800 \]
This simplifies to:
\[ \frac{9}{5}B = 1800 \]

**Hint:** Combine like terms to simplify the equation.

### Step 8: Solve for \( B \)
To solve for \( B \):
\[ B = 1800 \times \frac{5}{9} = 1000 \]

**Hint:** Use multiplication and division to find the value of \( B \).

### Step 9: Find \( G \)
Now that we have \( B \), we can find \( G \):
\[ G = 1800 - B = 1800 - 1000 = 800 \]

**Hint:** Always double-check your calculations to ensure accuracy.

### Conclusion
The number of girls in the school is:
\[ \boxed{800} \]