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

Options

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

Answer

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

1. **Determine the total number of students**:
The total number of students in the class is given as 70.

2. **Calculate the number of students who failed in Test I**:
Since 50% of the students failed in Test I:
\[ \text{Number of students failed in Test I} = 50\% \text{ of } 70 = \frac{50}{100} \times 70 = 35 \]

3. **Calculate the number of students who failed in Test II**:
Since 40% of the students failed in Test II:
\[ \text{Number of students failed in Test II} = 40\% \text{ of } 70 = \frac{40}{100} \times 70 = 28 \]

4. **Calculate the total number of students who failed at least one test**:
To find the number of students who passed both tests, we need to find the number of students who failed at least one test. We can use the principle of inclusion-exclusion here:
\[ \text{Number of students failed in at least one test} = \text{Number failed in Test I} + \text{Number failed in Test II} - \text{Number failed in both tests} \]
However, we do not have the number of students who failed both tests directly. For simplicity, we will assume that there are no students who failed both tests (which is a common assumption in such problems unless stated otherwise).

5. **Calculate the total number of students who passed both tests**:
Since we are assuming that no student failed both tests, we can calculate the number of students who passed both tests as follows:
\[ \text{Number of students passed in both tests} = \text{Total students} - (\text{Number failed in Test I} + \text{Number failed in Test II}) \]
\[ = 70 - (35 + 28) = 70 - 63 = 7 \]

Thus, the number of students who passed in both tests is **7**.