Question

The ratio of the number of men to the number of women at a concert is 5 : 3.The ratio of the number of women to the number of children is 2 : 5.Find the ratio of the number of children to the total number of women and men in the concert.

• A. 15 : 16
• B. 16 : 15
• C. 13 : 12
• D. 12 : 13

Answer 1

Answer: (A)

15 : 16

the ratio of the number of men to the number of women at a concert is $\frac{5}{3}$

let the ratio constant is $x$ for this ratio ,then no of men =$5x$

and the number of women is =$3x$

the ratio of the number of women to the number of children is =$\frac{2}{5}$

let the ratio for this ratio is $y$

then number of women is =$2y$

and number of children is = $5y$

no. of women = 3x=2y , x=$\frac{2y}{3}$

sum of women and men is = 2y+5x=$2y+5\times \frac{2y}{3}=\frac{16y}{3}$

then ratio of children to sum of women and men is =$\frac{5y}{\frac{16y}{3}}=\frac{15}{16}$

hence option$A$ is correct.