Discussion
If
\(p : q = 1 : 2\)
\(q : r = 4 : 3\)
\(r : s = 4 : 5\)
and \(u\) is 50% more than \(s\), what is the ratio \(p : u\)?
Answer: D
The ratio \(p : u\) is 16 : 45.
Chain the ratios with a common value. Take \(p = 1\); then \(q = 2\). From \(q : r = 4 : 3\), \(r = \frac{3}{4} \times 2 = 1.5\). From \(r : s = 4 : 5\), \(s = \frac{5}{4} \times 1.5 = 1.875\). And \(u = 1.5 \times 1.875 = 2.8125\).
\[ \frac{p}{u} = \frac{1}{2.8125} = \frac{16}{45} \]
The ratio \(p : s\) is 8 : 15; 16 : 15 doubles it instead of scaling \(s\) up by 1.5, and 2 : 15 and 1 : 5 do not follow from chaining the given ratios.
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