Question

The sum of the denominator of the fraction is 3 less than twice the denominator. If each of the numerator and denominator is decreased by 1., the fraction becomes 1/2. Find the fraction.

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Answer 1

Let the numerator be x and denominator be y.

Let the fraction be

y

x

x+y+3=2y

(or) x−y=−3

(or) x=y−3 _____ (1)

Also ,

y−1

x−1

=

2

1

x−1=

2

y−1

x=

2

y−1

+1⇒2x=y−1+2=y+1

(or) 2x−y=1 _____ (2)

substituting (1) in (2),

2(y−3)−y=1

⇒2y−6−y=1⇒y=7

put y=7 in (1) we get x=7−3=4

∴x=4,y=7

∴ the fraction is

y

x

=

7

4