Question

There are 3/5 as many men as women in the hall. 2/3 of the men and 1/5 of the women wear formal dress. What is the ratio of the people in the hall who do not wear formal dress to the total number of people in the hall ?

Answer 1

Ratio of people in the hall who do not wear formal dress to the total number  of people in the hall is 61:120.

• The number of men in the room the room be x .
• There are 3/5 as many men in the hall as women.

number of women = 3/5x

• Now, 2/3 of the men wear formal dress and 1/5 of the women wear formal dress.

Therefore , 2/3x of the total men wear formal dress and 3/25x of the total women wear formal dress.

• Now, men who do not wear formal dress are x - 2/3x = 1/3x.

• Now , women who do not wear formal dress = 3/5x - 3/25x = 12/25x.

• We have to find the ratio of people who do not wear formal dress to the total number of people in the hall.

• Number of people who do not wear formal dress = men who do not wear formal dress + women who do not wear formal dress = 1/3x + 12/25x = 61/75x.
• Total number of people = number of men +number of women = x + 3/5x = 8/5x.
• Now taking the ratio of the number of people wearing informal dress to the total number of people in the dress.
• Ratio = $\frac{\frac{61x}{75}}{\frac{8x}{5}}$ = 61/120

Answer 2

Step-by-step explanation:

Let number of women in the hall be x.

number of men in hall will be 3/5x.

total number of people (men+women) in hall= x+3/5x= 8x/5.

number of men wearing formal dress are 2/3 X 3/5 x = 2/5 x.

number of women wearing formal dress are 1/5 X x = x/5.

total number of people wearing formal dress= 2/5x +x/5=3/5x.

total number of people not wearing formal dress= total number of people in the hall - total number of people wearing formal dress

= 8/5x - 3/5x=5/5x=x.

Ratio of people not wearing formal dress to total number of people in hall is

x/1÷8x/5= x/1*5/8x= 5/8 = 5:8

the required ratio is 5:8 Answer.