SSC Selection Post 2020 PYQ — Question 69

The correct answer is option 3 i.e. 9 : 6 : 2.

 

[ (a + b) : (b + c) : (c + a) = 5 : 12 : 11 and  a + b + c = 28 ]

(a + b = 5x) , (b + c = 12x) , (c + a = 11x)

[ (a + b) + (b + c) + (c + a) = 5x + 12x + 11x = 28x ]

Totals up  :$[ 2(a + b + c) = 28x \Rightarrow a + b + c = \frac{28x}{2} = 14x ]$

from the question: $[ a + b + c = 28 \Rightarrow 14x = 28 \Rightarrow x = 2 ]$

⇒  x = 2

(a + b = 10) , (b + c = 24) , (c + a = 22)

⇒ (a + b = 10) , (a + c = 22) 

$[ (a + c) - (a + b) = 22 - 10 = c - b = 12 \Rightarrow c = b + 12 ]$

⇒(b + c = 24)
$(c = b + 12): [ b + (b + 12) = 24 \Rightarrow 2b + 12 = 24$

$\Rightarrow 2b = 12 \Rightarrow b = 6 \Rightarrow c = 6 + 12 = 18 \Rightarrow a + b = 10 \Rightarrow a = 10 – 6 = 4 ]$

(a = 4), (b = 6), (c = 18)

⇒ $\frac{1}{a} : \frac{1}{b} : \frac{1}{c} = \frac{1}{4} : \frac{1}{6} : \frac{1}{18}$

⇒ $\frac{36}{4} : \frac{36}{6} : \frac{36}{18} = 9 : 6 : 2$