Question

if 2 is added to the numerator of a fraction it reduces to 1 by 2 and if 1 is subtracted from the denominator it reduces to 1 by 3 find the fraction​

Answer 1

Answer:

Let the fraction be x/y

Given that

x+2/y =1/2 -----> equ i

x/y-1 =1/3 -----> equ ii

From i and ii

2(x+2) =1(y) -------> equ i

3(x) =1(y-1) -------> equ ii

=> 2x+4=y

3x=y-1

Subtract i and ii. we get

2x - y = -4

3x - y = -1

(-) (+) = (+)

______________

-x = -3

_____________

=> x=3

subtitute x=3 in equ i. we get

2(3+2)=y

=> 2(5) =y

=> y=10

Therefore the value of x and y are 3 and 10 respectively.

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.