Explanation

(c)
Equation of intersection of line is
$(100x + 50y - 1) + \lambda(75x + 25y + 3) = 0$
$\Rightarrow (100 + 75\lambda)x + (50 + 25\lambda)y = - 3\lambda$ …(i)
$\Rightarrow \frac{x}{\frac{1 - 3\lambda}{100 + 75\lambda}} + \frac{y}{\frac{1 - 3\lambda}{50 + 25\lambda}} = 1$
According to the given condition
$\frac{1 - 3\lambda}{100 + 75\lambda} = \frac{1 - 3\lambda}{50 + 25\lambda}$
$\Rightarrow \ 50 = - 50\lambda\ \Rightarrow \ \lambda = - 1$
$\therefore$ From Eq. (i), we get
$25x + 25y - 4 = 0$