Q18 of 168 Page 7

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

Let the denominator be ‘X’, so the numerator will be ‘(X+1)’.


the fraction is



On simplifying further,



30(2X2 + 2X + 1) = 61 (X2 + X)


60X2 + 60X + 30 = 61X2+ 61X


X2 + X – 30 = 0–––––– (i)


On applying Sreedhracharya formula







X= – 6 or 5


∴ X = 5 (Only positive values)


∴ Denominator is = 5 & numerator is (X+1) = 6


∴ The fraction is .


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