Question

At the start of a seminar, the ratio of the number of male participants to the number of female participants was 3 : 1. During the tea break, 16 participants left and 6 more female participants registered. The ratio of the male to the female participants became 2:1. The total number of participants at the start of the seminar was

• A. 64
• B. 48
• C. 54
• D. Data Insufficient

Hint:

In ratio problems, ensure you have enough information about the changes in both variables before trying to calculate the total.

Answer 1

The Correct Option is D

Let the number of male participants at the start be \( 3x \), and the number of female participants at the start be \( x \). After the tea break, 16 participants left, and 6 more females registered, so the number of male participants becomes \( 3x - m \) and the number of female participants becomes \( x - f + 6 \), where \( m \) and \( f \) are the number of males and females who left. The ratio of males to females after the tea break is given as 2:1, so: \[ \frac{3x - m}{x - f + 6} = 2 \] But we do not have enough information about \( m \) and \( f \), so the data is insufficient to calculate the total number of participants at the start. Thus, the answer is Data Insufficient.