GATE Civil 2022 Set 2 | GA Question: 2

Question

$x:y:z = \frac{1}{2} : \frac{1}{3} : \frac{1}{4}.$

What is the value of $\frac{x+z-y}{y} ?$

• A. $0.75$
• B. $1.25$
• C. $2.25$
• D. $3.25$

Answer 1

Given that$, x:y:z = \frac{1}{2}:\frac{1}{3}:\frac{1}{4}$

$\Rightarrow x:y:z = \frac{1}{2} \times 12:\frac{1}{3}\times 12:\frac{1}{4}\times 12 \quad [{\color{Blue}{\because \text{LCM(2,3,4) = 12}}}]$

$\Rightarrow x:y:z = 6:4:3 = k\;\text{(let)}$

$\Rightarrow \boxed{x = 6k, y = 4k, z = 3k}$

$\therefore$ The value of $\dfrac{x+z-y}{y} = \dfrac{6k+3k-4k}{4k} = \dfrac{5k}{4k} = 1.25.$

Correct Answer $:\text{B}$