Question

if we add 1 to numerator, and subtract 1 from the denomination, a fraction reduce the 1. it becomes ½ if we only add 1 to the denominator. what is the fraction?

Answer 1

Answer:

Required fraction=$\frac{x}{y}=\frac{3}{5}$

Step-by-step explanation:

Let the numerator = x,

denominator = y,

Required fraction = $\frac{x}{y}---(1)$

According to the problem given,

if we add 1 to numerator, and subtract 1 from the denomination,the fraction reduce the 1,we get

$\frac{x+1}{y-1}=1$

$\implies x+1=y-1$

$\implies x = y-1-1$

$\implies x = y-2 ---(2)$

And ,

If we add 1 to the denominator it becomes 1/2.

$\frac{x}{y+1}=\frac{1}{2}$

$\implies x = \frac{y+1}{2}--(3)$

/* from (1) & (2), we get

$y-2=\frac{y+1}{2}$

$\implies 2(y-2)=y+1$

$\implies 2y-4=y+1$

$\implies 2y-y=1+4$

$\implies y = 5$

Now, substitute y=5 in equation (2) ,we get

$\implies x = 5-2=3$

Therefore,

x=3, y=5

Required fraction=$\frac{x}{y}=\frac{3}{5}$

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Answer 2

Answer:

Step-by-step explanation:

Given :-

If we add 1 to numerator, and subtract 1 from the denomination, a fraction reduce the 1.

It becomes ½ if we only add 1 to the denominator.

To Find :-

The Fraction

Solution :-

Let the fraction be x/y                  

According to the question,

⇒ x + 1/y - 1 = 1                  

⇒ x - y = - 2 ... (i)

⇒ x/y + 1 = 1/2                  

⇒ 2x - y = 1 ... (ii)              

   

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

⇒ x = 3 ... (iii)            

     

Putting this value in equation (i), we get                  

⇒ 3 - y = - 2                  

⇒ -y =  5                  

⇒ y = 5                  

Hence, the fraction is 3/5