Question

at a function, the ratio of the number of men to the woman was 3: 4 . when another 5 men and 5 woman joined the function, the ratio became 7:9. how many men were there ay the function at first.​

Answer 1

Let the ration of men and women =x:y

Acceding to given question.

y

x

=

4

3

4x=3y

x=

4

3y

−−−−−−−−−−−(1)

Now,

5 men and 5 women joining the function.

So,

y+5

x+5

=

9

7

9x+45=7y+35

9x−7y=35−45

9x−7y=10

9x−7y+10=0−−−−−−−−−−−(2)

From equation (1) and (2) to

9×

4

3y

−7y+10=0

27y−28y+40=0

−y+40=0

−y=−40

y=40

Women =40

Put the value of y in equation (1) and we get

x=

4

3y

x=

4

3×40

x=3×10

x=30

Men =30

Hence, 30 men were there at the function at first.