Tk. 180 is to be divided among 66 persons (men and women). The ratio of the total amount of money received by men and women is 5 : 4. But the ratio of the money received by each man and woman is 3 : 2. The number of men is:

Question: Tk. 180 is to be divided among 66 persons (men and women). The ratio of the total amount of money received by men and women is 5 : 4. But the ratio of the money received by each man and woman is 3 : 2. The number of men is:

Solution:
Let, amount received by men = 5x.
and amount received by women = 4x

ATQ,
5x + 4x = 180
⇒ 9x = 180
⇒ x = 20

Amount received by men = TK.100
Amount received by women = TK.80

Suppose, the number of men be y and that of women be = (66 - y).
∴ (100/y)/{80/(66 - y)} = 3/2
⇒ (100/y) × {(66 - y)/80} = 3/2
⇒ {5(66 - y)}/4y = 3/2
⇒ 660 - 10y = 12y
⇒ 22y = 660
⇒ y = 30