90% of the students in a school passed in English, 85% passed in Mathematics and 150 students passed in both the subjects. If no student falled in both the sub jects, find the total number of stu dents.

Options

A. 120
B. 220
C. 200
D. 300

Answer

To solve the problem, we need to determine the total number of students in the school based on the given percentages and the number of students who passed both subjects.

### Step-by-Step Solution:

1. **Define Variables**: Let the total number of students in the school be \( x \).

2. **Calculate Students Passing English**: According to the problem, 90% of the students passed in English. Therefore, the number of students who passed in English is:
\[ \text{Students passing English} = 0.90x \]

3. **Calculate Students Passing Mathematics**: Similarly, 85% of the students passed in Mathematics. Thus, the number of students who passed in Mathematics is:
\[ \text{Students passing Mathematics} = 0.85x \]

4. **Students Passing Both Subjects**: We know that 150 students passed in both subjects.

5. **Use the Principle of Inclusion-Exclusion**: Since no student failed in both subjects, we can use the formula for the union of two sets:
\[ \text{Total passing either subject} = \text{Students passing English} + \text{Students passing Mathematics} - \text{Students passing both} \]
Substituting the values, we get:
\[ x = 0.90x + 0.85x - 150 \]

6. **Combine Like Terms**: Combine the terms on the right side:
\[ x = 1.75x - 150 \]

7. **Isolate \( x \)**: Rearranging the equation to isolate \( x \):
\[ 150 = 1.75x - x \]
\[ 150 = 0.75x \]

8. **Solve for \( x \)**: Divide both sides by 0.75 to find \( x \):
\[ x = \frac{150}{0.75} = 200 \]

9. **Conclusion**: The total number of students in the school is:
\[ \boxed{200} \]