If (a+b-c): (b+c-a): (a+c-b)=6:5:7, then 1/a:1/b:1/c is equal to:

If (a+b-c): (b+c-a): (a+c-b)=6:5:7, then 1/a:1/b:1/c is…

If (a+b-c): (b+c-a): (a+c-b)=6:5:7, then $\frac{1}{a}:\frac{1}{b}:\frac{1}{c}$ is equal to:

Show answer & explanation

Correct answer: B

Explanation

The correct answer is Option 2 i.e. 132:156: 143.

(a + b − c) : (b + c − a) : (a + c − b) = 6 : 5 : 7

Let a + b − c = 6k, b + c − a = 5k, a + c − b = 7k

Solve:
Add 1st and 2nd: 2b = 11k ⇒ b = 11k/2
Add 2nd and 3rd: 2c = 12k ⇒ c = 6k
Add 1st and 3rd: 2a = 13k ⇒ a = 13k/2

Then 1/a : 1/b : 1/c = 2/13k : 2/11k : 1/6k
Multiply all by LCM 858 ⇒ 132 : 156 : 143