Question

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

Answer 1

Given :-

• A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator.

To find :-

• Fraction

Solution :-

Let the required fraction be x/y

According to the question

• A fraction becomes 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 becomes 1/4 when 8 is added to its

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

Substitute the value of x in equation (ii)

→ 4x - y = 8

→ 4 × 5 - y = 8

→ 20 - y = 8

→ y = 20 - 8

→ y = 12

Hence,

• Required fraction = x/y = 5/12

Answer 2

Let ,

The fraction be " x/y "

First Condition :

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

Thus ,

(x - 1)/y = 1/3

3x - 3 = y

3x - y = 3 --- (i)

Second condition :

A fraction becomes 1/4 when 8 is added from the denominator

Thus ,

x/y + 8 = 1/4

4x = y + 8

4x - y = 8 --- (ii)

Subtract eq (i) from eq (ii) , we get

4x - y - (3x - y) = 8 - 3

x = 5

Put the value of x = 8 in eq (i) , we get

3(5) - y = 3

- y = 3 - 15

y = 12

$\sf \therefore \underline{The \: fraction \: is \: \frac{5}{12} }$