Question

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

Answer 1

Answer:

linear equations in two variables

Answer 2

Answer:

Step-by-step explanation

Given :-

2 is added to the numerator of a fraction it reduces to 1 by 2.

if 1 is subtracted from the denominator it reduces to 1 by 3.

To Find :-

The Fraction

Solution :-

Let the fraction be x/y .  

According to Question.

1st Equation

⇒ x+2/y = 1/2  

⇒ 2(x + 2) = y

⇒ 2x + 4 = y  

⇒ 2x - y = -4 ……(i)  

2nd Equation

⇒ x/y−1 = 1/3  

⇒ 3x = 1(y – 1)  

⇒ 3x – y = -1 ……(ii)  

On subtracting (i) from (ii)

⇒ x = (-1 + 4)

⇒ x = 3  

Putting x value in Eq (i),

⇒ 2x - y = -4

⇒ 2 × 3 – y = -4  

⇒ 6 – y = -4  

⇒ y = (6 + 4)

⇒ y = 10

Hence, the fraction is 3/10.