835, 734, 642, 751, 853, 981, 532

In each number except 383, the product of first and third digits is the middle one.

Each of the numbers except 72 is a perfect square.

Each of the numbers except 21 is an even number.

(1*1)+1 , (2*2)+1 , (3*3)+1 , (4*4)+1 , (5*5)+1 , (6*6)+1 , (7*7)+1 , (8*8)+1

But, 64 is out of pattern.

The pattern is 1 ², 2 ², 3 ², 4 ², 5 ², 6 ², 7 ². But, instead of 5 ², it is 20 which to be turned out.

Each of the numbers except 81 is a prime number.

Each of the numbers is a prime number except 12.

Let the speed of two trains be 7x and 8x km/hr.

Then, 8x =	❨	400	❩	= 100
		4

⟹ x =	❨	100	❩	= 12.5
		8

∴ Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr.

(1/2)x	+	(1/2)x	= 10
21		24

⟹	x	+	x	= 20
	21		24

⟹ 15x = 168 x 20

⟹ x =	❨	168 x 20	❩	= 224 km.
		15

Let the actual distance travelled be x km.

Then,	x	=	x + 20
	10		14

⟹ 14x = 10x + 200

⟹ 4x = 200

⟹ x = 50 km.