If \((a-b):(b-c):(c-d)=1:2:4\), then find the value of \(\displaystyle\frac{a-c}{b-d}\).
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\displaystyle\frac{1}{2}\)
The three differences are 1, 2 and 4 parts of one common amount, say \(t\). A longer difference such as \(a-c\) is the sum of the steps that make it up.
\(a-b=t\), \(b-c=2t\), \(c-d=4t\)
\(a-c=(a-b)+(b-c)=t+2t=3t\)
\(b-d=(b-c)+(c-d)=2t+4t=6t\)
\(\displaystyle\frac{a-c}{b-d}=\frac{3t}{6t}=\frac{1}{2}\)