Question

The numerator of a fraction is one more than its denominator. If its reciprocal is added to it the sum is 61/30. Find the fraction.

Answer 1

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

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  6/5.