Q21 of 168 Page 7

The denominator of a fraction exceeds its numerator by 3. If 3 is added to both numerator and denominator, the difference between the new and the original fraction is . Find the original fraction.

Let the denominator be ‘(X+3)’, so the numerator will be ‘X’.


the original fraction is


the new fraction is



On simplifying further,



88(9) = 9(X2 + 9X + 18)


X2 + 9X – 70 = 0 –––––– (i)


On applying Sreedhracharya formula







X = –14 or 5.


the numerator is X = 5 and denominator (X+3) will be 8 and the fraction will be , as taking (–14) will form a fraction i.e., (not satisfying the conditions) .


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