At a college entrance examination each candidate is admitted or rejected according to whether he has passed or failed the test. Of the candidates who are really capable, 80% pass the test and of the incapable, 25% pass the test. Given that 40% of the candidates are really capable, then the proportion of capable college students is about

Suppose there are 100 candidates for entrance.

∴ No. of capable candidates = 40 and No. of incapable candidates

= 100 – 40 = 60

Now, no. of capable candidates who pass the test

= 80% of 40 = 32

No. of incapable candidates who pass the test

= 25% of 60 = 15

Note that these successful candidates become college students.

Thus, there are 32+15 = 47 college students in all, of which 32 are capable.

Hence, Proportion of capable college students