m:n = \(2\frac{1}{3} : 1\frac{1}{5}\) and n : q = \(1\frac{1}{2} : 1\frac{1}{3}\), find q : m.

A.

35 : 18

B.

16 : 35

C.

18 : 35

D.

35 : 16

Correct answer is B

m:n = \(2\frac{1}{3} : 1\frac{1}{5}\) = m : n = \(\frac{7}{3} : \frac{6}{5}\)

\(\frac{7}{3} : \frac{6}{5}\) =  \(\frac{7}{3} \div \frac{6}{5}\)

\(\frac{m}{n}\) =  \(\frac{7}{3} \times \frac{5}{6}\)

\(\frac{m}{n}\) =  \(\frac{35}{18}\) = m =  \(\frac{35n}{18}\)

n : q = \(1\frac{1}{2} : 1\frac{1}{3}\) =  \(\frac{3}{2} : \frac{4}{3}\)

\(\frac{n}{q}\) =   \(\frac{3}{2} \times\frac{3}{4}\)

\(\frac{n}{q}\) =  \(\frac{9}{8}\) = q =  \(\frac{8n}{9}\) 

q : m =   \(\frac{8n}{9}\) :   \(\frac{35n}{18}\)

\(\frac{q}{m}\) =  \(\frac{8n}{9} \div \frac{35n}{18}\)

\(\frac{q}{m}\) =  \(\frac{8n}{9}\times\frac{18}{35n}\)

 =\(\frac{q}{m} = \frac{16}{35}\) = q : m = 16 : 35