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 answer
If
(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 Given that a + b + c = 27, we can substitute this into the equation to get:
2(27) = 18k 54 = 18k k = 54/18 = 3
Substituting k = 3 into 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 inverse of these values are:
1/a = 1/9, 1/b = 1/12, 1/c = 1/6
Therefore, the ratio 1/a : 1/b : 1/c is 1/9 : 1/12 : 1/6.
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