Question

Numerator of a fraction is 2 less than the denominator.if 1 is added to the numerator and 3 to the denominator then the becomes 2/3.find the original fraction
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Answer 1

Step-by-step explanation:

let the denominator be x

numerator = x-2

new numerator = x-2+1=3

new denominator=x+3

A.T.Q=

= x+3/x+3 = 2/3

after cross multiplying

we get =

= 3(x+3) = 2(x+3)

= 3x+9 = 2x+6

= 3x-2x = 6-9

= x = -3

numerator = -3-2

= -5

denominator= -3

original fraction = -5/-3

after cutting the (-) with (-)

original fraction = 5/3

Answer 2

GIVEN :–

• Numerator of a fraction is 2 less than the denominator.

• if 1 is added to the numerator and 3 to the denominator then the becomes ⅔ .

TO FIND :–

• Original fraction = ?

SOLUTION :–

• Let the denominator of fraction is 'x' then Numerator be (x - 2) .

$\\ \implies{ \bold{Fraction = \dfrac{x - 2}{x} }}$

• Now According to the question –

$\\ \implies{ \bold{ \dfrac{x - 2 + 1}{x + 3} = \dfrac{2}{3} }}$

$\\ \implies{ \bold{ \dfrac{x - 1}{x + 3} = \dfrac{2}{3} }}$

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

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

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

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

$\\ \implies \large { \boxed{ \bold{x =9}}}$

• Hence –

$\\ \implies{ \bold{Original \: \: Fraction = \dfrac{9 - 2}{9} }}$

$\\ \implies \large{ \boxed{ \bold{Original \: \: Fraction = \dfrac{7}{9} }}}$