# If 2 is Added to the Numerator of a Fraction, It Reduces to 1/2 and If 1 is Subtracted from the Denominator, It Reduces to 1/3. Find the Fraction. - Mathematics

Definition

If 2 is added to the numerator of a fraction, it reduces to 1/2 and if 1 is subtracted from the denominator, it reduces to 1/3. Find the fraction.

#### Solution

Let the numerator and denominator of the fraction be x and y respectively. Then the fraction is x/y

If 2 is added to the numerator of the fraction, it reduces to 1/2. Thus, we have

(x+2)/y=1/2

⇒ 2(x+2)=y

⇒ 2x+4 =y

⇒ 2x -y+4=0

If 1 is subtracted from the denominator, the fraction reduces to 1/3. Thus, we have

x/(y-1)=1/3

⇒ 3x = y-1

⇒ 3x -y +1=0

So, we have two equations

2x - y+4=0

3x -y +1=0

Here x and y are unknowns. We have to solve the above equations for x and y.

By using cross-multiplication, we have

x/((1-)xx1-1(-1)xx4)=(-y)/(2xx1-3xx4)=1/(2xx(-1)-3xx(-1))

⇒  x/(-1+4)=(-y)/(2-12)=1/(-2+13)

⇒  x/3=-y/-10=1/1

⇒  x/3=y/10=1

⇒  x/3= y/10=1

⇒  x=3,y=10

Hence, the fraction is3/10

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.8 | Q 8 | Page 89