Select the correct answerIf (a + b) : (b + c) : (c + a) = 7 : 6 : 5 and a + b + c = 27, then what will be the value of 1/a : 1/b : 1/c?
Question
Select the correct answerIf (a + b) : (b + c) : (c + a) = 7 : 6 : 5 and a + b + c = 27, then what will be the value of 1/a : 1/b : 1/c?
Solution
The given ratios can be written as:
a + b = 7k (1) b + c = 6k (2) c + a = 5k (3)
Adding equations (1), (2), and (3), we get:
2(a + b + c) = 18k a + b + c = 9k
But it is given that a + b + c = 27, so equating the two we get:
9k = 27 k = 3
Substituting the value of k in equations (1), (2), and (3), we get:
a + b = 21 b + c = 18 c + a = 15
Solving these equations, we get:
a = 9, b = 12, c = 6
The required ratio 1/a : 1/b : 1/c is therefore:
1/9 : 1/12 : 1/6 or 4 : 3 : 6.
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