Candidates in a competitive examination consisted of 60% men and 40% women. 70% men and 75% women cleared the qualifying test and entered the final test where 80% men and 70% women were successful.

Which of the following statements is correct?

The correct option is More men cleared the examination than women.

Let us break down the calculations step-by-step to understand why this statement is correct.

First, let the total number of candidates who appeared in the competitive examination be 100.

According to the given percentage distribution:
Number of men = 60% of 100 = 60
Number of women = 40% of 100 = 40

Step 1: Candidates who cleared the qualifying test

The problem states that 70% of men and 75% of women cleared the qualifying test:
Number of men clearing the qualifying test = 70% of 60 = $\frac{70}{100}\times 60=42$
Number of women clearing the qualifying test = 75% of 40 = $\frac{75}{100}\times 40=30$

Step 2: Candidates who cleared the final test (Successful candidates)

Out of those who entered the final test, 80% of the men and 70% of the women were successful:
Number of successful men = 80% of 42 = $\frac{80}{100}\times 42=33.6$
Number of successful women = 70% of 30 = $\frac{70}{100}\times 30=21$

Step 3: Verification of the statements

Let us compare the number of successful men and women:
Successful men = 33.6
Successful women = 21

Since 33.6 is greater than 21, more men cleared the examination than women. This makes the statement "More men cleared the examination than women" correct.

For completeness, let us verify the other options:
Total successful candidates = 33.6 + 21 = 54.6 out of 100.
This means the overall success rate is 54.6%, which is not below 50%. Thus, "Overall success rate is below 50%" is incorrect.
The success rate for men is $\frac{33.6}{60}\times 100=56\%$ and for women is $\frac{21}{40}\times 100=52.5\%$ . Since 56% is higher than 52.5%, the success rate is higher for men, making "Success rate is higher for women" incorrect.