Question

6.. A fraction becomes 1/3. when subtracted from the numerator and it becomes 1/4. when
8 is added to its denominator. Find the fraction.
(a) 4/12
(b) 3/13
(c) 5/12
(d) 11/7
Students life by Raushan Kumar
X Х​

Answer 1

Answer:

Let the fraction be x/y, where x is the numerator and y is the denominator

Fraction becomes 1/3 when 1 is subtracted from the numerator

(x - 1)/y = 1/3

y = 3 (x - 1)

y = 3x - 3 ..Eq..1

It becomes 1/4 when 8 is added to its denominator.

x/(y + 8) = 1/4

Cross multiplication

(y + 8) = 4x

4x = y + 8….Eq 2

Substituting the value of y from Eq. 1 to Eq. 2

4x = y + 8

4x = 3x - 3 + 8

4x - 3x = 5

x = 5

The numerator is 5

Substituting the value of x in Eq. 2 to derive the value of y

4x = y + 8

4 × 5 = y + 8

20 = y + 8

y = 20 - 8

y = 12

The denominator is 12.

The fraction is 5/12

,Answer: the fraction Is 5/12

Now checking the correctness of answer by subtracting 1 from the numerator

Fraction is 5/12

(5–1)/12 = 4/12 = 1/3

Means answer is correct

Answer 2

Correct question :-

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

Answer:-

Given :-

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

• It become 1/4 when 8 is added to its denominator.

To find:-

• The fraction.

Solution :-

Let the fraction be x/y     .

Then,  

⇒ x–1/y = 1/3                  

⇒ 3x – y = 3... (i)                  

⇒ x/y + 8 = 1/4                  

⇒ 4x – y = 8 ... (ii)                  

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

⇒ x = 5 ... (iii)                  

Putting this value in equation (i), we get                  

⇒ 15 – y = 3                  

⇒ y = 12                  

Hence, the fraction is 5/12.

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