Question

If the denominator of a fraction is increased by 8 we get 1/2 in its simplest form and the numerator is decreased by 1 the quotient obtained is 2 find the fraction

Answer 1

let the fraction be
$\frac{x}{y}$
denominator increased by 1
$\frac{x}{y + 8} = \frac{1}{2}$
numerator is decreased by 1

$\frac{x - 1}{y} = 2$
first equation = 2x = y + 8

second equation = x-1 = 2y

If u solve the equations

x = 5

y = 2

fraction = 5/2

Answer 2

Answer:

The Fraction is $\frac{5}{2}$

Step-by-step explanation:

Given: when denominator of a fraction increased by 8 we get $\frac{1}{2}$

          when numerator is decreased by 1 we get 2

To find: Fraction

Let the Fraction be $\frac{x}{y}$

So, According to the question we get

$\frac{x}{y+8}=\frac{1}{2}$

$2\timesx=1\times(y+8)$

$2x=y+8$

$2x-y=8$ .................. (1)

$\frac{x-1}{y}=2$

$x-1=2\times y$

$x=2y+1$

$x-2y=1$ ................... (2)

Now we solve equation (1) & (2) using substitution method

from equation (1),

y = 2x - 8

put this eqn (2), we get

x - 2 ( 2x - 8 ) = 1

x - 4x + 16 = 1

-3x + 16 = 1

-3x = 1 - 16

-3x = -15

x = 5 (by dividing -15 by -3)

⇒ y = 2 × 5 - 8 = 10 - 8 = 2

Therefore, The Fraction is $\frac{5}{2}$