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

Answer: Option A

Let the total number of candidates be x
Number of capable candidates who got admitted to college :
= 80% of 40% of x
$$\begin{array}{rl}& =\left(\frac{80}{100}\times \frac{40}{100}\times x\right)\\ & =\frac{8x}{25}\end{array}$$
Number of incapable college students :
= 25% of (100 - 40)% of x
$$\begin{array}{rl}& =\left(\frac{25}{100}\times \frac{60}{100}\times x\right)\\ & =\frac{3x}{20}\end{array}$$
Total number of candidates who got admitted to college :
$$=$$ $$\frac{8x}{25}$$ + $$\frac{3x}{20}$$
$$=$$ $$\frac{47x}{100}$$
∴ Required percentage :
$$\begin{array}{rl}& =\left(\frac{8x}{25}\times \frac{100}{47x}\times 100\right)\%\\ & =\left(\frac{3200}{47}\right)\%\\ & =68.09\%\approx 68\%\end{array}$$