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.

Correct Option

To determine the correct statement, we can assume a total number of candidates, for instance, 100.

• Number of men = 60% of 100 = 60.
• Men clearing the qualifying test = 70% of 60 = 42.
• Men successful in the final test = 80% of 42 = 33.6.

• Number of women = 40% of 100 = 40.
• Women clearing the qualifying test = 75% of 40 = 30.
• Women successful in the final test = 70% of 30 = 21.

Comparing the number of successful candidates: 33.6 men vs. 21 women. Since 33.6 > 21, more men cleared the examination than women. Thus, statement (3) is correct.

Incorrect Options

Let's evaluate the other options based on the calculated values:

• Option 1: Success rate is higher for women.
  • Men's success rate = (Number of successful men / Total men) × 100 = (33.6 / 60) × 100 = 56%.
  • Women's success rate = (Number of successful women / Total women) × 100 = (21 / 40) × 100 = 52.5%.
  Since 56% (men) > 52.5% (women), the success rate is higher for men, not women. Therefore, this statement is incorrect.
• Option 2: Overall success rate is below 50%.
  • Total successful candidates = 33.6 (men) + 21 (women) = 54.6.
  • Overall success rate = (Total successful candidates / Total candidates) × 100 = (54.6 / 100) × 100 = 54.6%.
  Since 54.6% is above 50%, this statement is incorrect.
• Option 4: Both (a) and (b) above are correct. As statements (1) and (2) are incorrect, this combined statement is also incorrect.