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

Answer:

Step-by-step explanation:

Let the numerator be x

Let denominator be y

According to given conditions

x/y+8=1/2

2x=y+8

2x-y=8 1.

x-1/y=2

x-1=2y

x-2y=1 2.

By elimination method

Multiply eq.2 by 2

2x-y=8-2x-4y=2

We get y=2 and x=5

Therefore fraction will be 5/2

Answer 2

Answer:

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

Step-by-step explanation:

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

So, According to the information given in 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),

$2x=8+y$

$x=\frac{y+8}{2}$ .................... (3)

put this in eqn (2), we get

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

$\frac{y+8-4y}{2}=1$

$y+8-4y=1\times2$

-3y + 8 = 2

-3y = 2 - 8

-3y = -6

y = 2 (by dividing -6 by -3)

now put value of y in Equation (3)

$\implies x=\frac{2+8}{2}=\frac{10}{2}=5$

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