Question

The sum of the numerator and denominator of a fraction is 12. If the denominator is increased

by 3, the fraction becomes 1/2. Find the fraction.​

Answer 1

Given,

• Sum of numerator & denominator = 12
• If denominator increased by 3, new fraction = ½

To find,

• Original fraction

Solution,

Let the numerator be N & denominator be D

AccordinG to Question :

⇒ N + D = 12

⇒ N = 12 - D ...(1)

2nd case :

⇒ N/(D + 3) = ½

⇒ D + 3 = 2N

[ Putting value from (1) ]

⇒ D + 3 = 2(12 - D)

⇒ D + 3 = 24 - 2D

⇒ D + 2D = 24 - 3

⇒ 3D = 21

⇒ D = 21/3

⇒ D = 7

∴ Denominator = 7

[ Putting this value in (1) ]

⇒ N = 12 - 7

⇒ N = 5

∴ Numerator = 5

Now findinG OriGinal fraction :

⇒ Original fraction = N/D

⇒ Original fraction = 5/7

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the numerator of the fraction to be x

And the denominator of the fraction to be y.

According to the Questions,

x + y = 12

⇒ x + y - 12 = 0 …… (i)

Putting this as an equation, we get

⇒ x/(y+3) = 1/2

⇒ 2x = (y+3)

⇒ 2x - y - 3 = 0 ....(ii)

Adding (i) and (ii), we get

⇒ x + y – 12 + (2x – y – 3) = 0

⇒ 3x -15 = 0

⇒ x = 5

Using x = 5 in (i), we get

⇒ 5 + y – 12 = 0

⇒ y = 7

Hence, the required fraction is 5/7.