Question

A fraction becomes $\frac{1}{3}$ if 1 is subtracted from both its numerator and denominator. It 1 is added to both the numerator and denominator, it becomes $\frac{1}{2}$. Find the fraction.

Answer 1

Given : 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.  

 

Solution:

Let the numerator and denominator of the fraction be x and y.  

Then , fraction =   numerator / denominator = x/y

Condition : 1

x - 1/y - 1 = 1/3

3(x - 1) = 1(y - 1)

3x - 3 = y - 1

3x - 3 + 1 = y

3x - 2 = y

y  = 3x - 2………….(1)  

Condition : 2

x + 1/y +  1 = 1/2

2(x + 1) = 1(y + 1)

2x + 2 = y + 1

2x + 2 - 1 = y  

2x + 1 = y  

y = 2x + 1 ………….(2)

On Substituting the value of y = 2x + 1 in equation (1) we obtain :  

y  = 3x - 2

2x + 1 = 3x - 2

2x - 3x = - 2 - 1

-x = - 3

x = 3

On putting x = 3 in eq (2)  we obtain :

y = 2x + 1

y = 2 (3) + 1

y = 6 + 1

y = 7

Now , fraction =  x/y = 3/7

Hence, the fraction is 3/7.

Hope this answer will help you…

 

Some more questions from this chapter :  

A fraction becomes 9/11 if 2 is added to both numerator and the denominator. If 3 is added to both the numerator and the denominator it becomes 5/6. Find the fraction

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The numerator of a fraction is 4 less than the denominator. If the numerator is decreased by 2 and denominator is increased by 1, then the denominator is eight times the numerator. Find the fraction.

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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 is 3/7.