Question

A math teacher gives her class two tests. 70% of the class passed both tests and 80% of the class passed the first test. What percent of those who passed the first test also passed the second test?

Answer 1

87.5% of those who passed the first test also passed the second test.

Lets assume, the total number of students in the class = X

As 80% of the class passed the first test, so the number of students passed the first test = 80% of X

`= (80)/(100)* X\\ \\ = 0.8X`

and the number of students passed both tests

= 70% of X

`= (70)/(100) * X\\ \\ = 0.7X`

It means, this 0.7X of those who passed the first test also passed the second test.

So, the percentage of 0.7X in respect of 0.8X is :

`(0.7X)/(0.8X) *100 \\ \\ = 0.875 *100 \\ \\ = 87.5%`

Thus, 87.5% of those who passed the first test also passed the second test.