Q20 of 168 Page 7

The denominator of a fraction exceeds its numerator by 3. If one is added to both numerator and denominator, the difference between the new and the original fractions 1 becomes . 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,



24(3) = X2 + 7X + 12


X2 + 7X – 60 = 0 –––––– (i)


On applying Sreedhracharya formula







∴ X = –12 or 5.


∴ the numerator is X = 5 and denominator (X+3) will be 8 and the fraction will be , as taking (–12) will form a fraction i.e., (not satisfying the conditions) .


More from this chapter

All 168 →
18

The numerator of a fraction is one more than its denominator. If its reciprocal is added to it the sum is . Find the fraction.

 19

The numerator of a fraction is 3 more than its denominator. If its reciprocal is subtracted from it, the difference is . Find the fraction.

 21

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.

 22

The numerator of a fraction is 3 less than denominator. If 2 is added to both 29 numerator as well as denominator, then sum of the new and original fraction is . Find the fraction.