Question : If $x:y=3:4$ and $y:z=3:4$ then $\frac{x+y+z}{3z}$ is equal to:
Option 1: $\frac{13}{27}$
Option 2: $\frac{1}{2}$
Option 3: $\frac{73}{84}$
Option 4: $\frac{37}{48}$
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Correct Answer: $\frac{37}{48}$
Solution : Given, $x:y=3:4$ and $y:z=3:4$ Now, $x:y=(3:4)×3=9:12$ and $y:z=(3:4)×4=12:16$ ⇒ $x:y:z=9:12:16$ So, the value of $\frac{x+y+z}{3z} = \frac{9+12+16}{3×16}=\frac{37}{48}$ Hence, the correct answer is $\frac{37}{48}$.
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