Question

If $(x+y):(y+z):(z+x)::5:11:12$, then $\frac{x}{y}=$

• A. $\frac{3}{2}$
• B. $\frac{2}{3}$
• C. $1$
• D. $0$

Answer 1

Answer: (A)

$\frac{3}{2}$

Solution - Given that $(x+y):(y+2):(z+x)\because 5:11:12$

This can be written as

$\begin{array}{c}x+y=5k-\left(1\right)\\ y+z=11k\text{or}z=11k-y\\ \text{and}z+x=12k\\ \Rightarrow 11k-y+x=12k\\ \Rightarrow x-y=k-\left(2\right)\end{array}$

$\begin{array}{c}\text{on solving (1) and (2) we get}\\ \begin{array}{c}x=3k\text{;}y=2k\\ \therefore \frac{x}{y}=\frac{3k}{2k}=\frac{3}{2}\end{array}\\ \text{Hence, (A) is the correct option.}\end{array}$