Q. 235.0( 6 Votes )

The numerator of a fraction is 2 less than the denominator. If 1 is added to both numerator and denominator the sum of the new and original fraction is . Find the original fraction.

Answer :

Given: Numerator of a fraction is 2 less than the denominator


To find: The fraction


Assumption: Let the denominator be x


Numerator = x – 2


Therefore, the fraction


If one is added to the numerator and denominator, fraction becomes


Sum of the fractions


Sum of the fractions


Therefore,



Taking L.C.M we get,





Cross-multiplying we get,


30x2 – 30x – 30 = 19x2 + 19x


30x2 – 19x2 – 30x – 19x – 30 = 0


11x2 – 49x – 30 = 0


Now we need to factorise such that, on multiplication we get 330 and on substraction we get 49.


So, equation becomes,


11x2 – (55x – 6x) – 30 = 0


11x2 – 55x + 6x – 30 = 0


11x(x – 5) + 6(x – 5) = 0


(11x + 6)(x – 5) = 0


So, 11x + 5 = 0 or x – 5 = 0




Putting these values in fraction


Hence, the possible fractions are,




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