If \((x-y):(y-z):(z-k)=2:3:5\), then find the value of \(\displaystyle\frac{y-k}{x-k}\).
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\displaystyle\frac{4}{5}\)
The three differences are 2, 3 and 5 parts of one common amount, say \(t\). A longer difference such as \(y-k\) is the sum of the steps that make it up.
\(x-y=2t\), \(y-z=3t\), \(z-k=5t\)
\(y-k=(y-z)+(z-k)=3t+5t=8t\)
\(x-k=(x-y)+(y-z)+(z-k)=2t+3t+5t=10t\)
\(\displaystyle\frac{y-k}{x-k}=\frac{8t}{10t}=\frac{4}{5}\)