Question

The sum of numerator and denominator of a fraction is greater by 1
than thrice the numerator. If the numerator is decreased by 1 then the
fraction reduces to
. Find the fraction.​

Answer 1

Let the numerator be x and the denominator be y.

From the given information, we have,

x+y=18and

y+2

x

=

3

1

or,x+y=18

=>y=18−x....(i)

Also,

y+2

x

=

3

1

=>3x=y+2

=>3x−y−2=0....(ii)

Solving by substitution method,

Substituting (i) in (ii), we get,

3x−y−2=0

=>3x−18+x−2=0

=>4x=20

=>x=5

Putting x=5 in equation (i), we get,

y=18−x

=>y=18−5

=>y=13

Thus, the original fractyion is

y

x

=

13

5