Question

The sum of the numerator and the denominator of a given fraction is 12. If 3 is added to its denominator, then the fraction becomes 1/2. Find the given fraction ​

Answer 1

$\bold\red{According~to~QueStion::}$

Let, Numerator = x & Denominator = y

Then,

i) Sum of Numerator and denominator equals to 12.

= > x+y = 12

ii) 3 is added to Denominator and then it equals to 1/2.

= > x+y/3 = 1/2

$\bold\pink{SoluTion::}$

Solving i) and ii) :-

In i):

x+y=12

=> x=12-y ---- (iii)

In ii):

x+y/3 = 1/2

=> (12-y) + y/3 = 1/2

=>{3(12-y)+y}/3 = 1/2

=> {36-3y+y}/3 = 1/2

=> {36-2y}/3 = 1/2

=> 2(36-2y) = 3×1 [Cross multiplication]

=> 72-4y = 3

=> 72-3 = 4y

=> 69 = 4y

Therefore, y = 69/4 = 17.25

$\bold\purple{Now,}$

In iii)

x = 12-y

=> x = 12-17.25

=> x = -5.25

$\bold\green{Hence,}$

Required fraction

= Numerator/Denominator = x/y

= -5.25/17.25

= -52500/172500 [Removed the decimal point after multiplying the numerator and denominator by 100]

= -525/1725 [ Cancelled the zeros ]

= -21/69 [ Cancelled the numbers by 25 ]

= -7/23 [ Cancelled the numbers by 3 ]

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${\underbrace{\overbrace{\mathcal{\red{Be~Brainly..!}}}}}$