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Question
If (m + n) : (n – m) = 5 : 2 ; m : n is ______.
Options
3 : 7
7 : 3
5 : 3
3 : 5
Solution
If (m + n) : (n – m) = 5 : 2 ; m : n is 7 : 3.
Explanation:
Given m + n : m – n = 5 : 2
`\implies (m + n)/(m - n) = 5/2`
Applying componendo and dividendo,
`(m + n + m - n)/(m + n - (m - n)) = (5 + 2)/(5 - 2)`
`\implies (2m)/(m + n - m + n) = 7/3`
`\implies (2m)/(2n) = 7/3`
`\implies m/n = 7/3`
`\implies` m : n = 7 : 3
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