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Math  /  Data & Statistics

QuestionIA physics master gave her class 2 tent. 30%30 \% of the class passed both test and 45%45 \% of the yy dass passed the 7 st test. What %\% of these who passed the 1st test also passed the 2nd test

Studdy Solution

STEP 1

1. Let the total number of students in the class be x x .
2. Let the number of students who passed both tests be 0.3x 0.3x .
3. Let the number of students who passed the first test be 0.45x 0.45x .
4. We need to find the percentage of students who passed the first test and also passed the second test.

STEP 2

1. Understand the relationship between the sets of students passing each test.
2. Calculate the percentage of students who passed both tests out of those who passed the first test.

STEP 3

Identify the number of students who passed both tests, which is given as 0.3x 0.3x .

STEP 4

Identify the number of students who passed the first test, which is given as 0.45x 0.45x .

STEP 5

Calculate the percentage of students who passed both tests out of those who passed the first test:
Percentage=(0.3x0.45x)×100%\text{Percentage} = \left( \frac{0.3x}{0.45x} \right) \times 100\%

STEP 6

Simplify the expression:
Percentage=(0.30.45)×100%=(23)×100%\text{Percentage} = \left( \frac{0.3}{0.45} \right) \times 100\% = \left( \frac{2}{3} \right) \times 100\%

STEP 7

Calculate the final percentage:
Percentage=66.67%\text{Percentage} = 66.67\%
The percentage of students who passed the first test and also passed the second test is:
66.67% \boxed{66.67\%}

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