Question

if 2 us Subtracted from the Numenator and 1 is added the denominator,a fraction becomes 1/2 but when 4 is added to the numerator and 3 is subtracted from the denominator it becomes 3/2 .Find the fraction​

Answer 1

Answer:

Step-by-step explanation:

Solution :-

Let the fraction be x/y.

According to the Question,

⇒ x - 2/y + 1 = 1/2

⇒ 2x - 4 = y + 1

⇒ 2x - y = 5 ... (i)

Also, x + 4/y - 3 = 3/2

⇒ 2x + 8 = 3y - 9

⇒ 2x - 3y = - 17 ....(ii)

Subtracting Eq (ii) from (i), we get

⇒ 2y = 22

⇒ y = 22/2

⇒ y = 11

Putting y's value in Eq (i), we get

⇒ 2x - 11 = 5

⇒ 2x = 11 + 5

⇒ 2x = 16

⇒ x = 16/2

⇒ x = 8

Hence, the required fraction is 8/11.

Answer 2

Answer :

8/11

Step by Step explanation :

Fraction = n/d

n - 2/d + 1 = 1/2

2(n - 2) = 1(d + 1)

2n - 4 = d + 1

2n - d = 4 + 1

2n - d = 5

n + 4/d - 3 = 3/2

2(n + 4) = 3(d - 3)

2n + 8 = 3d - 9

2n - 3d = -9 - 8

2n - 3d = -17

2n - 3d - 2n - d = -17 - 5

-2d = -22

d = 11

2n - d = 5

2n - 11 = 5

2n = 11 + 5

2n = 16

n = 8