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Question
If (a – b) : (a + b) = 1 : 11, find the ratio (5a + 4b + 15) : (5a – 4b + 3).
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Solution
(a – b) : (a + b) = 1 : 11,
`(a - b)/(a + b) = 1/11`
11a – 11b = a + b
10a = 12b
`a/b = 12/10 = 6/5`
So, let a = 6k and b = 5k
`(5a + 4b + 15)/(5a - 4b + 3) = (5(6k) + 4(5k) + 15)/(5(6k) - 4(5k) + 3)`
= `(30k + 20k + 15)/(30k - 20k + 3)`
= `(50k + 15)/(10k + 3)`
= `(5(10k + 3))/(10k + 3)`
= 5
Hence, (5a + 4b + 15) : (5a – 4b + 3) = 5 : 1
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