If (a + b) : (b + c) : (c + a) = 7 : 6 : 5 and a + b + c = 54, then what will be the value of \(\frac{1}{a}\) : \(\frac{1}{b}\) : \(\frac{1}{c}\) ?

4 : 3 : 6

(a + b) : (b + c) : (c + a) = 7 : 6 : 5    ......(ii)

Here, adding all,

⇒  2(a + b + c) = 18R

⇒  (a + b + c) = 9R = 54

⇒ 1R = 6

We can find the value of a, b and c:

⇒ a + b + c = 9R   .....(i)

(a + b) = 7R            .....(ii)

(b + c) = 6R             .....(iii)

(c + a) = 5R             .....(iv)

After subtracting from (i);

a = 3R; b = 4R; c = 2R

a : b : c = 3 : 4 : 2

Now,

⇒ \(\frac{1}{a}\) : \(\frac{1}{b}\) : \(\frac{1}{c}\) = \(\frac{1}{3}\) : \(\frac{1}{4}\) : \(\frac{1}{2}\) = 4 : 3 : 6