Question

A fraction becomes 1/3. When 1 is subtracted from the numerator and denominator. If 1 is added to both numerator and denominator. It becomes 1/2. Find the fraction​

Answer 1

Answer:

Fraction is 3/7

Step-by-step explanation:

Let numerator be x and denominator be y

$\frac{x-1}{y-1} = \frac{1}{3}$

3(x-1) = y-1

3x - 3 = y - 1

3x - y = -1 + 3

3x - y = 2

y = 3x - 2.......(1)

$\frac{x+1}{y+1} = \frac{1}{2}$

2(x+1) = y+1

2x + 2 = y + 1

2x - y = 1 - 2

2x - y = -1.......(2)

Substituting (1) in (2)

2x - ( 3x - 2) = -1

2x - 3x + 2 = -1

-x = -1 - 2

- x = -3

x = 3

Substituting x = 3 in (2)

2(3) - y = -1

6 - y = -1

6+1 = y

y = 7

Fraction is 3/7

Answer 2

Answer:

let the numerator and denominator be x and y

so eq will be

x-1/y-1= 1/3

x+1/y+1=1/2

by cross multiplication

3x-y=2

2x-y=0

by elimination method

3x-y=2

2x-y=0

x=2

put the value of x in eq 1

3(2)-y=2

6-y=2

-y=-4

y=4

fraction = 1/2