In class , 70 students wrote two tests, viz,. Test-I and Test-II. 50% of the students failed in Test-I and 40% of the students failed in Test-II. How many students passed in both the tests?

Options

A. 21
B. 7
C. 28
D. 14

Explanation

To solve the problem step by step, we can follow these calculations:

1. **Determine the total number of students**:
- Given that there are 70 students in total.

2. **Calculate the number of students who failed in Test-I**:
- 50% of the students failed in Test-I.
- Number of students who failed in Test-I = 50% of 70 = (50/100) * 70 = 35 students.

3. **Calculate the number of students who failed in Test-II**:
- 40% of the students failed in Test-II.
- Number of students who failed in Test-II = 40% of 70 = (40/100) * 70 = 28 students.

4. **Calculate the number of students who passed in both tests**:
- To find the number of students who passed both tests, we can use the following formula:
\[ \text{Number of students who passed both tests} = \text{Total students} - (\text{Students failed in Test-I} + \text{Students failed in Test-II}) \]
- However, we need to consider that some students may have failed both tests. To find the exact number of students who passed both tests, we can use the principle of inclusion-exclusion:
\[ \text{Number of students who passed both tests} = \text{Total students} - \text{Students failed in Test-I} - \text{Students failed in Test-II} + \text{Students failed in both tests} \]
- Since we do not have the number of students who failed both tests, we can assume that the students who failed in Test-I and Test-II are distinct for this calculation.
- Therefore, we can calculate:
\[ \text{Number of students who passed both tests} = 70 - 35 - 28 = 7 \]

5. **Final answer**:
- The number of students who passed in both tests is **7 students**.