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Question
If a : b = 9 : 10, find the value of `(5a + 3b)/(5a - 3b)`
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Solution
a : b = 9 : 10
⇒ `a/b = (9)/(10)`
`(5a + 3b)/(5a - 3b)`
= `((5a)/(b) + (3b)/(b))/((5a)/(b) - (3b)/(b))`
= `((5a)/(b) + 3)/((5a)/(b) - 3)` ...(Dividing by b)
= `(5 xx 9/10 + 3)/(5 xx 9/10 - 3)`
= `(9/2 + 3)/(9/2 - 3)`
= `(15/2)/(3/2)` ...(Substituting the value of `a/b`)
= `(15)/(2) xx (2)/(3)`
= 5
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