Question

A swimming club has 250 men and 170 women. If the number of women is decreased in the ratio 4:5 while the number of men is increased in the ratio 6:5, what is the new ratio of men to women?

a) 6:5
b) 5:6
c) 7:5
d) 5:7

Answer 1

7:5 is the new ratio of men to women.

Step-by-step explanation:

Initially, the swimming club had 250 men and 170 women. The number of women is decreased in the ratio (Option C)4:5, and the number of men is increased in the ratio 6:5. To determine the new ratio of men to women, we calculate the adjusted numbers.

For women, a decrease in the ratio of 4:5 means reducing the number by a factor of 4 + 5 = 9 parts. So, 170 women divided into 9 parts would mean each part represents 170 / 9 = 18.888..., approximately 19 women per part. Therefore, 4 parts represent 4 * 19 = 76 women after the decrease.

For men, an increase in the ratio of 6:5 means the number increases by a factor of 6 + 5 = 11 parts. So, 250 men divided into 11 parts would mean each part represents 250 / 11 = 22.727..., approximately 23 men per part. Therefore, 5 parts represent 5 * 23 = 115 men after the increase.

Hence, the new ratio of men to women is 115:76, which simplifies to 7:5 when both numbers are divided by their greatest common divisor of 19. Therefore, the correct answer is c) 7:5, representing the new ratio of men to women after the adjustments in the swimming club. (Option C)