Rs.180 are 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 man is

Suppose amount received by
men $= 5x.$
and amount received by women $= 4x$
According to question
$5x + 4x = 180$
$=> 9x = 180 => x = 20$
 Amount received by men $= rs 100$
Amount received by women$= 80$
Suppose the number of men be
$y$ and that of women be $(66 – y).$
According to question,

$\frac{\frac{100}{y}}{\frac{80}{66-y}}$ = $\frac{3}{2}$

$=> 660 – 10y = 12y$
$=> 22y = 660$

$=> y = 30$

Let the number of men be x.

Then, number of women = 66 - x

Money received by x men = (5/9) × (Rs. 180) = Rs. 100

Money received by (66 - x) women = Rs. 180 - Rs. 100 = Rs. 80

Ratio of money received by each man and woman = 3 : 2

According to the question, (100/x) : (80/(66 - x)) = 3/2,

After solving this, we get, 440x = 13200 ⇒ x = 30

Hence, total number of men is 30.

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