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:
A. 68%
B. 70%
C. 73%
D. 75%
Answer: Option A
Solution(By Examveda Team)
Let the total number of candidates be xNumber of capable candidates who got admitted to college :
= 80% of 40% of x
$$\eqalign{ & = \left( {\frac{{80}}{{100}} \times \frac{{40}}{{100}} \times x} \right) \cr & = \frac{{8x}}{{25}} \cr} $$
Number of incapable college students :
= 25% of (100 - 40)% of x
$$\eqalign{ & = \left( {\frac{{25}}{{100}} \times \frac{{60}}{{100}} \times x} \right) \cr & = \frac{{3x}}{{20}} \cr} $$
Total number of candidates who got admitted to college :
$$=$$ $$\frac{{8x}}{{25}}$$ + $$\frac{{3x}}{{20}}$$
$$=$$ $$\frac{{47x}}{{100}}$$
∴ Required percentage :
$$\eqalign{ & = \left( {\frac{{8x}}{{25}} \times \frac{{100}}{{47x}} \times 100} \right)\% \cr & = \left( {\frac{{3200}}{{47}}} \right)\% \cr & = 68.09\% \approx 68\% \cr} $$
Related Questions on Percentage
A. $$\frac{1}{4}$$
B. $$\frac{1}{3}$$
C. $$\frac{1}{2}$$
D. $$\frac{2}{3}$$
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