If $\dfrac{x}{a + b - c} = \dfrac{y}{b + c - a} = \dfrac{z}{c + a - b}$ = 5 and a + b + c = 7; the value of x + y + z is :

1. 35

2. $\dfrac{7}{5}$

3. $\dfrac{5}{7}$

4. 42

Given,

⇒ a + b + c = 7

⇒ a + b = 7 - c

⇒ b + c = 7 - a

⇒ c + a = 7 - b

Given,

$\phantom{\Rightarrow} \dfrac{x}{a + b - c} = 5 \\[1em] \Rightarrow \dfrac{x}{7 - c - c} = 5 \\[1em] \Rightarrow x = 5(7 - 2c). \\[2em] \phantom{\Rightarrow} \dfrac{y}{b + c - a} = 5 \\[1em] \Rightarrow \dfrac{y}{7 - a - a} = 5 \\[1em] \Rightarrow y = 5(7 - 2a). \\[2em] \phantom{\Rightarrow} \dfrac{z}{c + a - b} = 5 \\[1em] \Rightarrow \dfrac{z}{7 - b - b} = 5 \\[1em] \Rightarrow z = 5(7 - 2b). \\[1em]$

x + y + z = 5(7 - 2c) + 5(7 - 2a) + 5(7 - 2b)

= 35 - 10c + 35 - 10a + 35 - 10b

= 105 - 10(a + b + c)

= 105 - 10 × 7

= 105 - 70

= 35.

Hence, Option 1 is the correct option.