Question

A fraction becomes 1/3 when l is subtracted from the numerator and it becomes 1/4 when &
is added to its denominator. The fraction obtained is
(a)3/12
(b)4/12
(c)5/12 (a)7/12​

Answer 1

$\underline\red{\bold{Answer :-}}$ (C) 5/12

$\blue{\texttt{Given \: that :-}}$

If 1 is subtracted from the numerator fraction becomes 1/4

firstly , let Numerator be x

& denominator be y

so , fraction is $\: \large\frac{x}{y}$

Then,

$\large\frac{Numerator - 1}{Denominator} = \large\frac{1}{3}$

$\frac{x - 1}{y} = \large\frac{1}{3}$

$3(x - 1) = y$

$3x - y =3$ ____________(1)

Also, It 8 is added to denominator ,fraction becomes $\large\frac{1}{4}$

$\large\frac{Numerator \: }{Denominator + 8} = \large\frac{1}{4}$

$\large\frac{x}{y + 8} = \large\frac{1}{4}$

$4x = y + 8$

$4x - y = 8$ ___________(2)

$\blue{\texttt{from \: (1) ,}}$

$3x - y = 3$

$3x = y + 3$

$x = ( \large\frac{y + 3}{3})$

$\blue{\texttt{putting \: value \: of \: x \: in \: (2) ,}}$

$4x - y - 8 = 0$

$4 ( \large\frac{y + 3}{3}) - y - 8 = 0$

multiplying both sides by 3 ,

$3 \times 4x( \large\frac{y + 3}{3} ) - 3 \times y - 3 \times 8 = 3 \times 0$

$4(y + 3) - 3y - 24 = 0$

$4y + 12 - 3y - 24 = 0$

$y - 12 = 0$

$\underline\red{\bold{y \: = \: 12}}$

$\blue{\texttt{putting \: value \: of \: y \: in \: equation \: (1) ,}}$

$3x - y = 3$

$3x - 12 = 3$

$3x = 12 + 3$

$3x =15$

$x = \large\frac{15}{3}$

$\underline\red{\bold{x \: = \: 5}}$

Therefore ,

$\blue{\texttt{x \: = \: 5}}$

$\blue{\texttt{y \: = \: 12}}$ , is the solution.

so , $\blue{\texttt{numerator \: = \: x \: = \: 5}}$

$\blue{\texttt{denominator \: = \: y \: = \: 12}}$

$original \: fraction \: = \large\frac{Numerator}{Denominator} = \frac{x}{y}$

$= \large\frac{5}{12}$

Answer 2

Answer:

Given :-

If 1 is subtracted from the numerator fraction becomes 1/4

To Find :-

Fraction

Solution :-

Let us assume the fraction be x/y

x-1/y = ⅓

By Cross Multiplication

3(x -1) = 1(y)

3(x - 1) = y

3x - y = 3 (1)

Now,

When 8 added

x/ y + 8 = ¼

4x - y + 8 (2)

From equation 1

3x - y = 3

3x = y + 3

x = y + 3/3

Now,

Putting x

4(y + 3/3) - y - 8 = 0

Now,

Multiplying LHS and RHS by 3

3 × 4x(y + 3/3) - 3 × y - 3 × 8 = 3 × 0

4x(y + 3/3) - 3 × y - 3 × 24 = 0

4x (y + 1) - 3 × y - 3 × 24 = 0

4( y + 3) - 3y - 24 = 0

4y + 12 - 3y - 24 = 0

4y - 3y - 24 - 12 = 0

y - 12 = 0

y = 12 + 0

y = 12

Now,

Finding x

3x - y = 3

3x - 12 = 3

3x = 12 + 3

3x = 15

x = 15/3

x = 5

Therefore :-

Fraction is 5/12.