If a : (b + c) = 1 : 3 and c : (a + b) = 5 : 7, then b : (a + c) is equal to –
2022
If a : (b + c) = 1 : 3 and c : (a + b) = 5 : 7, then b : (a + c) is equal to –
- A.
1 : 2
- B.
2 : 1
- C.
2 : 3
- D.
1 : 3
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Correct answer: A
Given: a : (b + c) = 1 : 3 and c : (a + b) = 5 : 7
From a : (b + c) = 1 : 3, we get b + c = 3a.
From c : (a + b) = 5 : 7, we get c = (5/7)(a + b).
Substitute b = 3a − c into c = (5/7)(a + b):
c = (5/7)[a + (3a − c)] = (5/7)(4a − c).
So c = (20/7)a − (5/7)c ⇒ c + (5/7)c = (20/7)a ⇒ (12/7)c = (20/7)a.
Therefore 12c = 20a, so c = (5/3)a.
Now b = 3a − c = 3a − (5/3)a = (4/3)a.
Compute b : (a + c) = (4/3)a : [a + (5/3)a] = (4/3)a : (8/3)a = 4 : 8 = 1 : 2.
Therefore, b : (a + c) = 1 : 2.