Question

7. The numerator of a fraction is 3 less than its denominator. If 1 is added
to the denominator, the fraction is decreased by
1
15
Find the fraction.
[CBSE 2012]​

Answer 1

Answer:

Let the denominator be x then numerator be (x-3)

fraction =

x

x−3

It is added ⇒

x+1

x−3

=

x

x−3

−

15

1

(by the condition)

⇒

x+1

x−3

=

15x

15x−45−x

.

⇒

x+1

x−3

=

15x

14x−45

⇒15x

2

−45x=14x

2

−45x+14x−45

⇒x

2

−14x+45=0

⇒x

2

−9x−5x+45=0

⇒x(x−9)−5(x−9)=0

⇒x−5=0,x−9=0

∴x=5,9.

If x = 9 ⇒ fraction =

9

9−3

=

9

6

=

3

2

If x = 5 ⇒ fraction =

5

5−3

=

5

2

Hence . the fraction is

5

2

or

3

2