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MAT Exam 2024 Paper

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Question : 80 of 150

Marks: +1, -0

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-

64
48
54
Data Insufficient

Solution:

Concept:

The gender split of the 16 participants who left is not given, so the final ratio alone cannot determine the initial total.

Explanation:

Let initial male participants be

3x

and female participants be

x

.

So, initial total

= 3x + x = 4x

.

Suppose

a

male participants left during the tea break.

Then female participants who left

= 16 - a

.

After 6 more female participants registered:

Male participants

= 3x - a

Female participants

= x - (16 - a) + 6 = x - 10 + a

Given final ratio is

2 : 1

, we get:

\frac{3x - a}{x - 10 + a} = \frac{2}{1}

3x - a = 2x - 20 + 2a

x = 3a - 20

So, initial total

= 4x = 12a - 80

.

Since the value of

a

is not known, the initial total cannot be uniquely determined.

Answer:

D. Data Insufficient

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