If (2ab - b2) : (6a2 - ab) = 1 : 6, then what is the value of (a + b) : (a - b)?
-5 or 5
Given:
(2ab - b2) : (6a2 - ab) = 1 : 6
Calculation:
We have,
(2ab - b2) : (6a2 - ab) = 1 : 6
⇒ 6 × (2ab - b2) = 1 × (6a2 - ab)
⇒ 12ab - 6b2 = 6a2 - ab
⇒ 6a2 - 13ab + 6b2 = 0
⇒ 6a2 - 9ab - 4ab + 6b2 = 0
⇒ 3a (2a - 3b) - 2b (2a - 3b) = 0
⇒ (2a - 3b) (3a - 2b) = 0
⇒ (2a - 3b) = 0 or (3a - 2b) = 0
⇒ 2a = 3b or 3a = 2b
Case:1 2a = 3b
⇒ a : b = 3 : 2
⇒ (a + b) : (a - b) = (3 + 2) : (3 - 2)
⇒ (a + b) : (a - b) = 5
Case:2 3a = 2b
⇒ a : b = 2 : 3
⇒ (a + b) : (a - b) = (2 + 3) : (2 - 3)
⇒ (a + b) : (a - b) = -5
∴ The value of (a + b) : (a - b) is -5 or 5.
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In population of a city the ratio of men and women is 12 : 11. If total population of that city is 4,60,000, then the population of women is:
