Given that p:q = (frac{1}{3}):(frac{1}{2}) and q:r = (frac{2}{5}), find p:r

Given that p:q = (frac{1}{3}):(frac{1}{2}) and q:r = (frac{2}{5}), find p:r

Correct Answer: Option B

Explanation

(p : q = frac{1}{3} : frac{1}{2})

(frac{p}{q} = frac{2}{3})

(2q = 3p … (1))

(q : r = frac{2}{5} : frac{4}{7})

(frac{q}{r} = frac{2}{5} times frac{7}{4} = frac{7}{10})

(10q = 7r … (2))

Eliminating q, we have

(1) : (2q = 3p )

(10q = 15p)

(implies 15p = 7r)

(therefore frac{p}{r} = frac{7}{15})

(p : r = 7 : 15)