Question

A fraction becomes 1/3 if 1 is subtracted from both its numerator and denominator. If 1 is added

to both the numerator and denominator, it becomes 1/2. Find the fraction.
step by step instructions required otherwise reported​

Answer 1

Given,

• 1 substracted from both numerator & denominator ,fraction = 1/3
• 1 added to botg numerator & denominator,fraction = 1/2

To find,

• Original fraction = ?

Solution,

Let the numerator be N & denominator be D

Case 1 :

→ (N - 1)/(D - 1) = 1/3

→ D - 1 = 3(N - 1)

→ D - 1 = 3N - 3

→ D = 3N - 3 + 1

→ D = 3N - 2 - Eq. ( l )

Case 2 :

→ (N + 1)/(D + 1) = ½

→ D + 1 = 2(N + 1)

→ D + 1 = 2N + 2

→ D = 2N + 2 - 1

→ D = 2N + 1 - Eq. ( ll )

★ Comparing both equations :

→ 3N - 2 = 2N + 1

→ 3N - 2N = 1 + 2

→ N = 3

∴ Numerator = 3

[ Put this value in Eq.( ll) ]

→ D = 2(3) + 1

→ D = 6 + 1

→ D = 7

∴ Denominator = 7

Now findinG OriGinal fraction :

⇒ Original fraction = N/D

⇒ Original fraction = 3/7

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the numerator be x

And the denominator be y.

According to the Question,

1st Equation,

⇒ (x - 1)/(y - 1) = 1/3

⇒ 3x - 3 = y - 1

⇒ 3x - y = 2 

⇒ y = 3x - 2 .....(i)

2nd Equation,

⇒ (x + 1)/(y + 1) = 1/2

⇒ 2x + 2 = y + 1

⇒ y - 2x = 1 .......(ii)

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

⇒ 3x - 2 - 2x = 1

⇒ x - 2 = 1

⇒ x = 1 + 2

⇒ x = 3

Putting x's value, we get

⇒ y = 7

Hence, the given fraction is x/y = 3/7.