Question

a fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when it is added to its denominator find the fraction.

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Answer 1

Answer:

Let the numerator =x

and the denominator =y

So, the fraction =

y/x

According to the question,

Condition I:

x−1

=

3

1

⇒3(x−1)=y

⇒3x−y=y

⇒3x−y−3=0 ..(i)

Condition II:

y+8

x

=

4

1

⇒4x=y+8

⇒4x−y=8

⇒4x−y−8=0...(ii)

By cross-multiplication method, we have

⇒

8−3

x

=

−12+24

y

=

−3+4

1

⇒

5

x

=

12

y

=

1

1

I II III

On taking I and III ratio, we get

⇒

5

x

=

1

1

⇒x=5

On taking II and III ratio, we get

⇒

12

y

=

1

1

⇒y=12

So, the numerator is 5 and the denominator is 12

So, the numerator is 5 and the denominator is 12Hence, the fraction is

12

_

5

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