Question

If we add 1 to the numerator and subtract 1 from the denominator a fraction reduces to 2. It becomes 1/2 if we only add 1 to the denominator.What is the fraction??
Note: it reduces to 2 not 1.

Answer 1

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

Answer 2

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CORRECT QUESTION :

If we add 1 to the numerator and subtract 1 from the denominator a fraction reduces to 2.

It becomes 1/2 if we only add 1 to the denominator

.What is the fraction??

Note: it reduces to 2 not 1.

SOLUTION :

Let the Numerator is the fraction be a

The denominator of the fraction is b

Therefore the Fraction is $\dfrac{a}{b}$

New Fraction becomes -

$\dfrac{a+1}{b-1} = \dfrac{2}{1} \\ \\ => 2b - 2 = a + 1 ......... ( 1 )$

$\dfrac{a+1}{b} = \dfrac{1}{2} \\ \\ => 2a + 2 = b ......... ( 2 )$

Solving, a = 3 , b = 5

Hence the original Fraction : $\dfrac{3}{5}$