Question

A fraction becomes 1/3 if 1 is subtracted from both the numerator and denominator. of 1 is added to both the numerator and denominator,it becomes 1/2.find the fraction

Answer 1

let numerator be x and denominator be y
⇒x-1/y-1=1/3
⇒3x-y=2......................(i)

⇒x+1/y+1=1/2
⇒2x-y=2.........................(ii)
(i)-(ii)

⇒x=3
putting it in (i),
⇒3-1/y-1=1/3
⇒6=y-1
⇒y=7

Answer 2

Solution -

Let us assume, x be the numerator and y be the denominator of a fraction.

Therefore, given fraction is x/y

Given:

(x-1) / (y-1) = 1/3

3x - 3 = y - 1

3x - y = 2 

y = 3x - 2 -------------------1

Also given:

(x+1) / (y+1) = 1/2

2x + 2 = y + 1

y - 2x = 1 -------------2

Substitute the value of y from equation 1

3x - 2 - 2x = 1

x - 2 = 1

x = 1 + 2

x = 3

Therefore, y = 3x - 2 = 3 * 3 - 2 = 7

y = 7

Therefore, the given fraction is x/y = 3/7