The number of integral points lie inside the triangle are
1. If x = 1, then y may be 1, 2, 3, ....., 39
2. If x = 2, then y may be 1, 2, 3, ....., 38
3. If x = 3, then y may be 1, 2, 3, ....., 37
$$ \vdots $$
39. If x = 39, then the value of y is 1.
Hence, the number of interior points are
$$1 + 2 + 3 + .... + 39 = {{39 \times 40} \over 2} = 780$$Since the point of intersection lies on fourth quadrant and equidistant from the two axes,
i.e., let the point be (k, $$-$$k) and this point satisfies the two equations of the given lines.
$$\therefore$$ 4ak $$-$$ 2ak + c = 0 ......... (1)
and 5bk $$-$$ 2bk + d = 0 ..... (2)
From (1) we get, $$k = {{ - c} \over {2a}}$$
Putting the value of k in (2) we get,
$$5b\left( { - {c \over {2a}}} \right) - 2b\left( { - {c \over {2a}}} \right) + d = 0$$
or, $$ - {{5bc} \over {2a}} + {{2bc} \over {2a}} + d = 0$$ or, $$ - {{3bc} \over {2a}} + d = 0$$
or, $$ - 3bc + 2ad = 0$$ or, $$3bc - 2ad = 0$$