Question

if we add 1 the numerator and subtract 1 from the denominator, a fraction reduces to 1 . It becomes 1/2 if we only add 1 to the denominator. what is the fraction? ​

Answer 1

$\huge \tt \underline{ \underline \blue{answer : }}$

Let the numerator be 'x' and denominator be 'y'.

Fraction is (x/y).

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♣ If one is added to numerator and one is substracted from denominator, fraction reduces to one.

$\to \tt{ \frac{x + 1}{y - 1} = 1} \\ \\ \to \tt{x + 1 = 1(y - 1)} \\ \\ \to \tt {x + 1 = y - 1} \\ \\ \to \tt \red{x - y = - 2} \: \: \: \: \: (equation \: 1)$

♣ If one is added to denominator , fraction becomes

1/2.

$\tt{ \to \: \frac{x}{y + 1} = \frac{1}{2} } \\ \\ \to \tt{2(x) = 1(y + 1)} \\ \\ \to \tt{2x = y + 1} \\ \\ \to \tt \red{2x - y = 1} \: \: \: \: \: (equation \: 2)$

➟Substracting equation 1 by 2 ,

2x-y-(x-y) = 1-(-2)

2x-y-x+y = 1+2

➻ x = 3

➥Putting the value of 'x' in equation (1) we get,

x-y = -2

3-y = -2

-y = -5

➻ y = 5

➯Fraction is 3/5.