In a party hall, there are people in blue and red dresses. The ratio of the number of men in blue to the number of women in red is 3 : 7. The ratio of the number of  men in red to the number of women in blue is 2 : 1. If the ratio of number of people in blue to the number of people in red is 35 : 76, then what is the ratio of number of men to the number of women?

52 : 59

The ratio of the number of men in blue to the number of women in red = 3 : 7.

The ratio of the number of men in red to the number of women in blue = 2 : 1.

⇒ Number of people in blue = $3x + y$  (from the two ratios)

   Number of people in red = $7x + 2y$

According to the question, the ratio of number of people in blue dresses to the number of people in red dresses = 35 : 76

⇒ $\frac{3x+y}{7x+2y} = \frac{35}{76}$

⇒`($3x + y$) x 76 = ($7x + 2y$)x 35

⇒ 228$x$ + 76$y$ = 245$x$ + 70$y$

⇒             17$x$    =    6$y$

 $x$  :  $y$  = 6  : 17

No. of males = 3$x$ + 2$y$ = 3 x 6 + 2 x 17 = 18 + 34 = 52

No. of women = 7$x$ + $y$ = 7 x 6 + 17 = 42 + 17 = 59

Ratio = 52 : 59