Subject
Quantitative Aptitude
Topic
Ratio
If a + b + c = 1 and ab + bc + ca = ⅓ then a : b : c is
If a + b + c = 1 and ab + bc + ca = ⅓ then a : b : c is
ক)
1 : 2 : 2খ)
2 : 1 : 2গ)
1 : 1 : 1ঘ)
1 : 2 : 1ঙ)
1 : 3 : 1Explanation
Given that, a + b + c = 1 and ab + bc + ca = ⅓ Then, ⇒ 3ab + 3bc + 3ca = a + b + c ⇒ a(3b – 1) + b(3c – 1) + c(3a – 1) = 0 Since a, b, c are non-zero terms, ⇒ (3b – 1), (3c - 1) and (3a - 1) must be zero ⇒ a = b = c = ⅓ ⇒ a : b : c = ⅓ : ⅓ : ⅓ Or, a : b : c = 1 : 1 : 1Related questions
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