Since the three digit number is divisible by 10, then the unit's digit is 0

Let the three digit number = $$a b 0$$

After the digits are interchanged, the new number is also divisible by 10, thus only a and b are interchanged.

=> New number = $$b a 0$$

Difference between number is divisible by 40

=> $$(100a + 10b) - (100b + 10a) = 40 k$$    (k is constant)

=> $$90a - 90b = 90 (a - b) = 40 k$$

=> k = $$\frac{9\left(a-b\right)}{4}$$

Since k is a natural number (a-b) should be a multiple of 4

If a = 9 , the values of b that satisfies the given equation are 1,5

If a = 8 , the value of b that satisfies the given equation is 4

If a = 7 , the values of b that satisfies the given equation is 3

If a = 6 , the values of b that satisfies the given equation is 2

If a = 5 , the values of b that satisfies the given equation is  1

The number could be = 510,620,730,840,950, 910

Thus, there are 6 numbers that satisfy these conditions.