Question

The sum of numerator and denominator of a fraction is 30. If 2 is

added to numerator and 2 is subtracted from denominator, then it

becomes 2/3. Find the fraction.​

Answer 1

Answer:

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Answer 2

Solution :

Let ,

numerator be x

denominator be y

So , fraction becomes $\sf \dfrac{x}{y}$

The sum of numerator and denominator of a fraction is 30

⇒ x + y = 30

⇒ x = 30 - y ... (1)

If 2 is added to numerator and 2 is subtracted from denominator , then it becomes 2/3

$\to \sf \dfrac{x+2}{y-2}$=$\dfrac{2}{3}$

sub. (1) here ,

$\begin{gathered}\to \sf \dfrac{(30-y)+2}{y-2}=\dfrac{2}{3}\\\\\to \sf \dfrac{32-y}{y-2}=\dfrac{2}{3}\\\\\to \sf 3(32-y)=2(y-2)\\\\\to \sf 96-3y=2y-4\\\\\to \sf 5y=100\\\\\leadsto \sf \red{y=20}\ \; \bigstar\end{gathered}$

3(32−y)=2(y−2)

96−3y=2y−4

5y=100

y=20

Sub. y value in (1) ,

⇒ x = 30 - (20)

⇒ x = 10

So , Fraction is , $\sf \red{\dfrac{x}{y} =\dfrac{10}{20}}$