Question

The mean age of a combined group of men and women is 30 years. if the mean age of group of men is 32 ànd that of the group of women is 27. find out ratio of men and women in group.​

Answer 1

Answer:

3:2

Step-by-step explanation:

Solution :-

Let the number of men be X

Let the number of women be Y

We know that

Mean = Sum of all observations/Number of all observations

The mean age of group of men = 32

=> Mean age group of men = Sum of all ages of men/Number of men

=> 32 = Sum of all ages of men /X

=> Sum of all ages of men = 32X

The mean age of group of women = 27

=> Mean age group of women = Sum of all ages of women/Number of women

=> 27 = Sum of all ages of women /Y

=> Sum of all ages of women = 27Y

Given that

The mean age of a combined group of men and women = 30 years.

=> Mean = Sum of all ages of both men and women / Number of men and women

=> 30 = (32X+27Y)/(X+Y)

=> 30(X+Y) = 32X+27Y

=> 30X+30Y = 32X+27Y

=> 32X+27Y-30X-30Y = 0

=> (32X-30X)+(27Y-30Y) = 0

=> (2X) + (-3Y) = 0

=> 2X-3Y = 0

=> 2X = 3Y

=> X/Y = 3/2

=> X:Y = 3:2

=> The ratio of number men and women = 3:2

Answer:-

The ratio of the number of men and the number of women in the group is 3:2

Used formulae:-

→Mean = Sum of all observations/Number of all observations

→ a:b can be written as a/b