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Question

The denominator of a fraction is 1 less than twice its numerator. If 1 is added to numerator and denominator respectively, the ratio of numerator to denominator is 3:5 Find the fraction.


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Solution

Step 1.Let the numerator of fraction be x.

Therefore denominator =2x-1

So, the fraction is x2x-1

Step 2.According to question if 1 is added to numerator and denominator respectively, the ratio of numerator to denominator is 3:5

Therefore we have ,

(x+1):(2x-1+1)=3:5(x+1):2x=3:5

x+12x=355(x+1)=3x2x5x+5=6x5x-6x=-5-x=-5x=5

Therefore numerator of the fraction is 5

Step 3. Now the denominator =2x-1

=2x5-1=10-1=9

Therefore the denominator of the fraction is 9

Hence the fraction is 59


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