Question

A fraction becomes 1/3 when 1 is subtracted from the numerator andit becomes 1 upon 4 when it is added to its denominator find the fraction

Answer 1

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✴ 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.

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➡ The original fraction is 5/12.

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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 original fraction.

Calculation :-

Let us consider our original fraction be, x/y    

             According to the question,      

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

⇒ x–1/y = 1/3                  

⇒ 3x – y = 3... (i)                  

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

⇒ x/y + 8 = 1/4                  

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

Subtracting equation (ii) from (i),

 4x – y = 8 ... (ii)    

 3x – y = 3... (i)      

- + -

_____________

x. = 5

____________

⇒ x = 5 ... (iii)                  

Putting this value in equation (i), we get                

⇒ 3x – y = 3... (i)                

⇒ 3 × 5 – y = 3... (i)                

⇒ 15 – y = 3                  

⇒ y = 12                  

Hence, the fraction is x/y , where x is 5 & y is 12.

Therefore, our fraction is 5/12.

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⚠ $\mathcal{\large {\underline{\orange{Important\:Note:-}}}}$

❌A fraction becomes 1/3 when 1 is subtracted from the numerator andit becomes 1 upon 4 when it is added to its denominator find the fraction

✔✔✔✔✔✔✔✔✔✔✔✔✔✔✔✔✔✔✔✔

• Avoid grammatical errors in question.
• Provide correct data in your question.
• I found correct answer from class 7th Maths text book.
• Ask questions properly.

Regards,

TheAdvancedHacker,

❂ComputerMaster

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Answer 2

Answer :-

Let the numerator = x

Let the denominator = y

Now, 

fraction becomes = x/y

According to the first condition,     

(x − 1)/y = 1/3

⇒y = 3x − 3    ......(1)

According to the second condition,   

 x/(y + 8) = 1/4

⇒y + 8 = 4x

⇒y = 4x − 8     .........(2)

from (1) and (2),    

  3x − 3 = 4x − 8

⇒3x − 4x = −8 + 3

−x = −5

⇒x = 5

Using  (1), we get

y = 15 − 3 = 12

So, the  fraction of the question is  = 5/12.

Thank you ✨