Question

A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to it’s denominator. Find the fraction ​

Answer 1

Given :-

• A fraction becomes 1/3 when 1 is subtracted from the numerator.

• It becomes 1/4 when 8 is added to it’s denominator.

To Find :-

• What's the fraction?

Solution :-

Let the fraction be x/y

According to the question :

Given that,

A fraction becomes 1/3 when 1 is subtracted from the numerator.

Therefore,

(x -1)/y = 1/3

⟼ 3x -y = 3........... eq(1)

Again, it’s given that

It becomes 1/4 when 8 is added to it’s denominator.

Hence,

x /(y+8) = 1/4

⟼ 4x -y =8..........eq(2)

Now, subtract eq(1) from eq(2)

4x -y =8

3x -y = 3

_________

$x = 5$

Put the value of x in eq(2)

4x -y =8

⟼ 4 × 5 -y = 8

⟼ y = 12

Therefore, the fraction is = 5/12

Answer 2

Answer:

Given :

A fraction become 1/3 when 1 is subtracted from the numerator and it become 1/4 when 8 is added to it's denominator.

To find :

The fraction

Solution :

Let the required fraction be x/y

A fraction become 1/3 when 1 is subtracted from the numerator

→ x - 1/y = ⅓

→ 3(x - 1) = y

→ 3x - 3 = y

→ 3x - y = 3 ----(i)

It become 1/4 when 8 is added to it's denominator.

→ x/y + 8 = ¼

→ 4x = y + 8

→ 4x - y = 8 -----(ii)

Subtract both the equations

→ 3x - y - (4x - y) = 3 - 8

→ 3x - y - 4x + y = - 5

→ - x = - 5

→ x = 5

Put the value of x in eqⁿ (ii)

→ 4x - y = 8

→ 4 × 5 - y = 8

→ 20 - y = 8

→ y = 20 - 8

→ y = 12

•°• Required fraction = x/y = 5/12

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