Discussion
\(x : y : z = \frac{1}{2} : \frac{1}{3} : \frac{1}{4}\).
What is the value of \(\frac{x+z-y}{y}\)?
Answer: B
The value is 1.25.
Clear the fractions by multiplying the ratio by 12, the LCM of 2, 3 and 4:
\[ \begin{aligned} x : y : z &= 6 : 4 : 3 \\ \frac{x + z - y}{y} &= \frac{6 + 3 - 4}{4} = \frac{5}{4} = 1.25 \end{aligned} \]
0.75 is \(3/4\), the ratio z : y alone. 2.25 is \((x + z)/y = 9/4\), forgetting to subtract y, and 3.25 is \((x + y + z)/y = 13/4\), adding y instead of subtracting it.
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