Question

A fraction 7/5 when 2 is substracted form Numerator and
it becomes 4/5 when 8 is added to its denominator , find the fraction​

Answer 1

Answer:

$\frac{92}{55}$

Step-by-step explanation:

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

The question states:

$i)$  When $2$ is substracted from the numerator the fraction becomes $\frac{7}{5}$

⇒ $\frac{x-2}{y}= \frac{7}{5}$

⇒ $5(x-2) = 7y$

⇒ $5x - 10 = 7y$

⇒ $5x - 7y - 10 = 0$                        --$(1)$

$ii)$  When 8 is added to the denominator the fraction becomes $\frac{4}{5}$

⇒ $\frac{x}{y+8} = \frac{4}{5}$

⇒ $5x = 4(y+8)$

⇒ $5x = 4y+32$

⇒ $5x - 4y - 32 = 0$                         --$(2)$

Substracting $(1)$ from $(2)$

⇒ $5x - 4y - 32 -(5x-7y-10) = 0$

⇒ $5x-4y-32-5x+7y+10 = 0$

⇒ $3y - 22 = 0$

⇒ $3y = 22$

⇒ $y = \frac{22}{3}$

Substituting in $(1)$

⇒$\frac{x-2}{\frac{22}{3} } = \frac{7}{5}$

⇒ $x-2 = \frac{7}{5}(\frac{22}{3})$

⇒ $x-2 = \frac{154}{15}$

⇒ $x = \frac{154}{15} + 2$

⇒ $x = \frac{154 + 30}{15}$

⇒ $x = \frac{184}{15}$

⇒ $\frac{x}{y} = \frac{\frac{184}{15} }{\frac{22}{3} }$

⇒ $\frac{x}{y} = \frac{184}{15}*\frac{3}{22}$

⇒ $\frac{x}{y} = \frac{92}{55}$