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

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

View answer & explanation

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

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