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Question
If a : b = 3 : 11, find (15a – 3b) : (9a + 5b). a
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Solution
a : b = 3 : 11 or `a/b = (3)/(11)`
Now `(15a - 3b)/(9a + 5b)`
= `((15a)/b - (3b)/(11))/((9a)/b + (5b)/b` ...(Dividing by b)
= `((15a)/b - 3)/(9a/b + 5)`
= `(15 xx (3)/(110 - 3))/(9 xx (3)/(11) + 5)` ...(Substituting the value of `a/b)`
= `(45/11 - 3)/(27/11 + 5)`
= `((45 - 33)/(11))/((27 + 55)/(11)`
= `((12)/(11))/((82)/(11)`
= `(12)/(11) xx (11)/(82)`
= `(12)/(82)`
= `(6)/(41)`
∴ (15a – 3b) : (9a + 5b) = 6 : 41.
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