In a party hall, there are people in blue and red dresses. The ratio of number of men in blue to the number of women in red is 3 : 7. The ratio of men in red to the number of women in blue is 2 : 1. If the ratio of the 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?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 52 : 59.
Let the number of men in blue to the number of women in red be 3x and 7x.
Now,
Number of men in red to the number of women in blue be 2y and y.
Total person in blue = 3x + y
Total person in red = 7x + 2y
According to the question;
⇒ (3x + y)/(7x + 2y) = 35/76
⇒ 17x = 6y
⇒ x/y = 6/17
Total men = 3x + 2y = 3 × 6 + 2 × 17 = 18 + 34 = 52
Total women = 7x + y = 7 × 6 + 17 = 42 + 17 = 59
Hence, the required ratio is 52 : 59.