Question

The denominator of a fraction is 3 more than its numerator if numerator and denominator both are increased by 2 the new fraction becomes 2 / 3 find the fraction

Answer 1

Step-by-step explanation:

Let the numerator be X

So, denominator is X+3

if both are increased by 2 the fraction will be X+2/X+5

So, according to the question the new fraction is 2/3and 2/3=X+2/X+5

BY CROSS MULTIPLICATION:-

3*(X+2)=2*(X+5)

3x+6=2x+10

3x-2x=10-6

x=4, this is numerator because we have considered x as numerator

X+3=4+3=7, this is denominator

SO THE FRACTION IS 4/7

HOPE THIS HELPS YOU

Answer 2

$\huge{\bf{\underline{\purple{Solution :}}}}$

Suppose the Numerator of fraction be x

According to Question First Case  :

∵Denominator of fraction is 3 more than its numerator .

∴Denominator of fraction = x + 3

Therefore,

Fraction Obtained = $\bold{\frac{x}{x +3}}$

According to Question Second Case :

∵If numerator and denominator both are increased by 2 then fraction become $\bold{\frac{2}{3}}$.

∴ $\implies \bold{\frac{x + 2}{(x +3) + 2} = \frac{2}{3}}$

$\implies \bold{\frac{x + 2}{x + 5} = \frac{2}{3}}$

$\implies \bold{3(x +2) = 2(x +5)}$

$\implies \bold{3x + 6 = 2x + 10}$

$\implies \bold{3x - 2x = 10 - 6}$

$\implies \boxed{\bold{ x = 4}}$

Therefore,

⇒The fraction = $\bold{\frac{4}{4 + 3}}$ = $\bold{\frac{4}{7}}$

Verified :

The fraction = $\bold{\frac{4}{7}}$

∴Denominator is three more than its numerator  & Numerator and denominator in two increased so fraction become 2/3 so check this condition satisfied or not :

⇒4 is numerator and 7 is denominator so 7 - 3 = 4 so First condition satisfied

Now Second Condition :

$\implies \bold{\frac{4 + 2}{7 + 2} = \frac{6}{9} = \frac{2}{3}}$

Also Satisfied So Answer is correct .

$\rule{200}2$