If (a-b) : (a+b) =1:11 , find the ratio (5a+4b+15) : (5a-4b+3) .

Given,
( a – b)/(a + b) = 1/11

We need to findthe ratio of (5a + 4b +15) :(5a -4b +3)

Solution

On dividing given equation LHS by b both by nominator and dinominator, we get

=(a/b – b/b)/(a/b + b/b) = 1/11

=>(a/b -1)/( a/b + 1)=1/11

= 11(a/b) -11 =a/b + 1

=10(a/b) =12

a/b =6/5

5a=6b

Let us assume that a =6k
b= 5k

Substituting the value in (5a + 4b +15) :(5a -4b +3) we get,

={ 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 : 1

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