Question

the denominator of a fraction is 12 more than the numerator. if 16 added both the numerator and the denominator, the new fraction so obtained is 10/13.find the original fraction.​

Answer 1

given:

the denominator of a fraction is 12 more than the numerator

let the numerator be x and denominator be x+12

so the fraction is => x/x+12

If 16 is added to both the numerator and denominator than the new fraction will be 10/13

=> x+16/x+12+16 = 10/13

=> x+16/x+28 = 10/13

by cross multiplying

=> 13(x+16) = 10(x+28)

=> 13x+208 = 10x+280

=> 13x-10x = 280-208

=> 3x = 72

=> x = 72/3

=> x = 24

so x/x+12

=> 24/24+12

=> 24/36

so the original fraction is 24/36

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