The following ratios are given: \(a : b = 2 : 3\) \(b : c = 4 : 5\) \(c : d = 3 : 2\) \(d : e = 5 : 4\) What is the value of the ratio a : e?
1 : 1
The combined ratio \(a:e\) is obtained by multiplying all the given ratios together:
\(\frac{a}{e} = \frac{a}{b} \times \frac{b}{c} \times \frac{c}{d} \times \frac{d}{e} = \frac{2}{3} \times \frac{4}{5} \times \frac{3}{2} \times \frac{5}{4}\).
Simplifying, \(\frac{2 \times 4 \times 3 \times 5}{3 \times 5 \times 2 \times 4} = 1\).
So \(a:e = 1:1\).
Hence, the ratio a : e is 1 : 1.
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