If $6x-10y=10$ and $\frac{x}{x+y}=\frac{5}{7}$, then $(x-y)$ is equal to:

3

The correct answer is Option (4) → 3

Simplify the second equation:

$\frac{x}{x + y} = \frac{5}{7}$

Cross-multiply to find the relationship between $x$ and $y$:

$7x = 5(x + y)$

$7x = 5x + 5y$

$2x = 5y ⇒x = \frac{5}{2}y \text{ or } x = 2.5y$

Substitute this into the first equation:

The first equation is $6x - 10y = 10$. Substituting $x = 2.5y$:

$6(2.5y) - 10y = 10$

$15y - 10y = 10$

$5y = 10$

$y = 2$

Find the value of $x$:

Using $x = 2.5y$:

$x = 2.5 \times 2 = 5$

Calculate $(x - y)$:

$x - y = 5 - 2 = 3$

Final Answer:

The value of $(x - y)$ is 3.