Question : If (x + y) : (y + z) : (z + x) = 3 : 5 : 7 and (x + y + z) = 45, then what is the value of z?
Option 1: 18
Option 2: 30
Option 3: 27
Option 4: 20
Correct Answer: 27
Solution :
Given: $(x + y)$, $(y + z)$, and $(z + x)$ = $3:5:7$ respectively.
Let $x + y = 3k$
$y + z = 5k$
$z + x = 7k$
Where $k$ is a constant.
Also, $x + y + z = 45$
Adding $(x+y)+(y+z)+(z+x)$, we get:
$2(x + y + z) = 15k$
Putting the value of $x + y + z = 45$, we get:
$⇒2\times45 = 15k$
$\therefore k = 6$
Now, Putting the value of $k$, we get:
$x + y = 18$
$y + z = 30$
$z + x = 42$
$\therefore z=(x + y + z)-(x + y)=45-18= 27$
Hence, the correct answer is 27.
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