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

A.
4:105 
B.
7:15 
C.
20:21 
D.
2:35 
E.
3:20
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)