Question

the numerator of a fraction is one more than its denominator if its reciprocal is subtracted from it the difference is 11/30 find the fraction

Answer 1

Given data:

Let the denominator be D

Numerator = D+1

Original fraction = Numerator/Denominator = (D+1)/D

New fraction is the reciprocal of original fraction = D/(D+1)

Difference = {(D+1)/D } – { D/(D+1)} = 11/30

Solution:

On solving the above equation,

{(D+1)^2 – D^2 } / D(D+1) = 11/30

(D^2+ 2D + 1 – D^2 ) / (D^2+D) = 11/30

60 D + 30 = 11D^2+ 11 D

= > 11D^2 - 49D - 30 = 0

This can also be written as:

11D^2 - 55D + 6D – 30 = 0

11D(D-5) + 6(D-5) = 0

(D-5) (11D+6) = 0

D-5=0

= > Denominator = 5

Fraction = (5+1)/5

Original Fraction = 6/5