Question

Solve the following pair of equations:

$\frac{25}{x+y}-\frac{3}{x-y}=1$ and $\frac{40}{x+y}+\frac{2}{x-y}=5$,

• A. $x=8,y=6$
• B. $x=4,y=6$
• C. $x=6,y=4$
• D. None of these

Answer 1

The correct option is C $x=6,y=4$

$\frac{25}{x+y}-\frac{3}{x-y}=1,\frac{40}{x+y}+\frac{2}{x-y}=5$

Let, $\frac{1}{x+y}=m$ and $\frac{1}{x-y}=n$
$25m-3n=1$ ...(1)
$40m+2n=5$ ...(2)
Multiply eq(1) by 2 and eq(2) by 3 and add
$50m+120m=17$
$m=\frac{1}{10}$
Hence, $n=\frac{1}{2}$
Thus, $x+y=10$
an $x-y=2$
or, $x=6,y=4$