Question

At a 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 now became 2:1. What was the total number of
participants at the start of the seminar ?
(a) 64 (6) 48 (c) 54
(d) T
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Answer 1

Given :  At a 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 now became 2:1.

To find : What was the total number of  participants at the start of the seminar

Solution:

At a start of a seminar, the ratio of the number of male  participants to the number of female participants was 3:1.

Males = 3M

Females = M

Total  = 4M

During the tea break 16 participants left and 6 more female  participants registered

=> Total = 4M - 6  + 16   = 4M - 10

in 16 Left

Females left  =  F  then Males left = 16 - F

=> F ≤  M  

Males Left  = 3M  - (16-F)  =  3M + F - 16

Females Now = M - F + 6

The ratio of the male to the female  participants now became 2:1.

(3M + F - 16 ) / (M - F + 6 )  =  2/1

=> 3M + F - 16 = 2M - 2F + 12

=> M + 3F  = 28

M + 3F  = 28

M = 7  , 10  , 13  ,  16 , 19  , 22  ,  25   , 28

total number of  participants at the start of the seminar  = 4M

28 , 40  , 52 , 64 ,  76 , 88 , 100 , 112

out of given option  64 is the only answer

64 is the total number of  participants at the start of the seminar

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