Given:
The ratio of men dressed in blue to women dressed in red = 1:6
The ratio of men dressed in red to women dressed in blue = 3:2
The ratio of people dressed in blue to people dressed in red = 37:87
Formula used:
Total people dressed in blue = Men in blue + Women in blue
Total people dressed in red = Men in red + Women in red
Let the number of men dressed in blue = x
Let the number of women dressed in red = 6x
Let the number of men dressed in red = 3y
Let the number of women dressed in blue = 2y
Ratio of people dressed in blue to red: 6x+3yx+2y=8737
Calculations:
From the given ratio: 6x+3yx+2y=8737
⇒ Cross multiplying: 87(x+2y)=37(6x+3y)
⇒ 87x+174y=222x+111y
⇒ 174y−111y=222x−87x
⇒ 63y=135x
⇒ xy=63135=715
Now, the total number of men = Men in blue + Men in red = x+3y
Total number of women = Women in blue + Women in red = 2y+6x
Substitute y=715x into the expressions:
Total men = x+3(715x)=x+745x=752x
Total women = 2(715x)+6x=730x+6x=772x
Ratio of men to women: 772x752x=7252=1813
∴ The correct answer is option (4).