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If (a + b - c) : (b + c - a) : (a + c - b) = 6 : 5 : 7, then \(\frac{1}{a}:\frac{1}{b}:\frac{1}{c}\) is equal to1. 156 : 132 : 1432. 132 : 156 : 1433. 156 : 143 : 1324. 143 : 156 : 132 |
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Answer» Correct Answer - Option 2 : 132 : 156 : 143 Given: (a + b - c) : (b + c - a) : (a + c - b) = 6 : 5 : 7 Concept used: Ratio and proportion Calculation: Let, a + b - c = 6k b + c - a = 5k a + c - b = 7k Adding all the above three equations we get, ⇒ a + b + c = 18k Adding (a + b + c) + (a + b - c) = 18k + 6k = 24k ⇒ a + b = \(\frac{{24k}}{2}\) = 12k Adding (a + b + c) + (b + c - a) = 18k + 5k = 23k ⇒ b + c = \(\frac{{23k}}{2}\) We have a + b + c = 18k and a + b = 12k ⇒ (a + b + c) - (a + b) = 18k - 12k ∴ c = 6k Where b + c = \(\frac{{23k}}{2}\) ⇒ b = \(\frac{{23k}}{2}\) - 6k ∴ b = \(\frac{{11k}}{2}\) We have a + b = 12k ⇒ a = 12k - \(\frac{{11k}}{2}\) ∴ a = \(\frac{{13k}}{2}\) So we have a = \(\frac{{13k}}{2}\), b = \(\frac{{11k}}{2}\), c = 6k ⇒ \(\frac{{132\ :\ 156\ :\ 143}}{{13 \times 11 \times 6}}\) ∴ Ans :- 132 : 156 : 143
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