Let n^th minima of 400 nm wave coincides with m^th minima of 560 nm wave.

Then,

(2n-1)(400/2) - (2m-1)(560/2)

2n-1 /2m-1  = 7/5 =14/10 ....

2n-1= 7

n= 4

2m-1=5

m=3

That is, 4^th minima of 400 nm wave coincides with 3^rd minima of 560 nm wave.

Location of this minima is-

y₁ =[ (2×4-1).(1000).(400×10^-6 ) ] / 2×0.1           (given,d=0.1 )

= 14 mm

Next 11^th minima of 400 nm wave will coincides with 8^th minima of 560 nm wave.

Location of this second minima is-

y₂ = [(2×11-1).(1000).(400×10^-6 )] /2×0.1

= 42 mm

So, the distance  between two sucessive regions of complete darkness is -

y₂ - y₁ = 42-14 = 20 mm