Question

the ratio of the number of men and women in a room is 7:8. if the percentage increases in the number of men and women be 20% and 10% respectively. what will be the new ratio

Answer 1

Step-by-step explanation:

Given :-

The ratio of the number of men and women in a room is 7:8. The percentage increases in the number of men and women be 20% and 10% respectively.

To find :-

What will be the new ratio ?

Solution :-

Given that

The ratio of the number of men and women in a room = 7:8

Let they be 7X and 8X

The number of men = 7X

The number of women = 8X

If the number of men is increased by 20% then the new number of men

=> 7X +20% of 7X

=> 7X +(20/100)×7X

=> 7X +(1/5)×7X

=> 7X +(7X/5)

=> (35X+7X)/5

=> 42X/5

If the number of women is increased by 10% then the new number of women

=> 8X +10% of 8X

=> 8X +(10/100)×8X

=> 8X +(1/10)×8X

=> 8X +(8X/10)

=> 8X+(4X/5)

=> (40X+4X)/5

=> 44X/5

The new ratio of the number of men and number of women in the room

=> (42X/5) : (44X/5)

=> (42X/5)/(44X/5)

=> (42X/5)×(5/44X)

=> (42X×5)/(5×44X)

=> 42X/44X

=> 42/44

=> 21/22

=> 21:22

Answer:-

The new ratio of the number of men and number of women in the room is 21:22

Used formulae:-

→ a:b can be written as a/b