I need help working out a statistic question

Question

Learner drivers a flunking a new tough practical test with fewer than half now making it through. The restricted test was changed last month to make it more of a challenge. With nearly 1500 tests completed, the overall pass rate had dropped from 80% from the old test to 39%. The current pass rate is 63% 

How was the data collected and explain the pass rates of 39%, 80% and 63%

Answer 1

It seems like the data was collected by sorting all 1500 tests into old tests and new tests. Then, the number of passed old tests was used to calculate the overall pass rate for the old test and the number of passed new tests was used to calculate the overall pass rate for the new test. The number of total passed tests was used to calculate the overall pass rate of the test ("current pass rate").

 

These pass rates mean that 80% of learners passed the old test, 39% of learners pass the new test, and at the moment, 63% of people who have taken either version have passed. As time goes on, if the new test is not changed, the current pass rate of 63% will drop lower and lower until it effectively reaches 39%.

 

You can use this information to figure out how many people have taken the new test (N) and how many have taken the old test (O) so far:

 

N + O = 1500

0.8(O) + 0.39(N) = 0.63(1500)

 

0.8(1500 - N) + 0.39(N) = 0.63(1500)

1200 - 0.41(N) = 945

-0.41(N) = -255

N = 622

 

O = 1500 - N

O = 1500 - 622

O = 878