Question

If the numerator of a fraction is increased by 2
and denominator is decreased by 1, it
becomes 2/3 If the numerator is increased by 1
and denominator is increased by 2, it becomes 1/3
Find the fraction.

در​

Answer 1

Answer:

X=2

y=7

Step-by-step explanation:

therefore the fraction will be 2/7

Answer 2

Answer:

Let the numerator be x

and let the denominator be y

CASE 1 :

numerator increased by 2 = x+2

denominator decreased by 1 =  y-1

result = 2\3

Equation = x+2\ y-1 = 2\3

     Now , cross multiply :

     3[x+2] = 2[y-1]

  3x+ 6 = 2y - 2

3x -2y +6+2 =0

3x- 2y + 8 = 0 = 3x - 2y = -8 ----------Eq [1]

CASE 2 :

Numerator increased by 1 = x+1

denominator increased by 2 = y+2

result = 1\3

Equation = x+1\y+2 = 1\3

    now , cross multiply :

 3[x+1] = 1[ y+2]

3x +3 = y+2

3x - y = 2-3

3x - y = -1 -------------Eq [2]

Now , subtract both the equations that is [2] - [1]

                 3x-y= -1                     [ in subtraction changes of signs take place]

                 3x -2y = -8

           --------------------------

                  y = 7

Now from eq [2]

3x-[7] = -1

3x = -1+7

3x = 6

x = 6\3 = 2

Hence the required value of x and y is 2 and 7 respectively

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