Question

The mean age of a combined group of men and women is 30 years. If the mean of the age of men and women are respectively 32 and 27, then the percentage of women in the group is

(A)30
(B)40
(C)50
(D)60

Answer 1

$\huge{\boxed{\red{\boxed{\mathfrak{\pink{Solution}}}}}}$

Let there be x women out of 100 persons.

Number of men = 100 - X

Given that mean of combined age of men and women = 30

Therefore, $\frac{32(100-x)+27x}{100} \:= \:30$

= 32 (100 - x) + 27x = 30 × 100

= 3200 - 32x + 27x = 3000

= -5x = 3000 - 3200

= -5x = -200

= x = -200/-5

or x = 40

Answer : (B) 40

Answer 2

Answer:

$suppose \: \: the \: \: ratio \: \: is \: \: k : 1\\ \\ = > \frac{32 \times k + 1 \times 27}{2} = 30 \\ \\ = > 32k + 27 = 60 \\ \\ = > 32k = 33 \\ \\ = > \frac{k}{1} = \frac{33}{32} \\ \\ = > women \: \: ratio = \frac{32}{65} \times 100 \\ \\ \: \: \: \: \: \: \: \: \: \: \: = 4 9.23 = 50(app.)$

Answer : (C)