My approach is to eliminate the wrong options and thus finding the correct option.
We have to find the number of red marbles Kallu have.
As Kallu having red marbles and black marbles in a ratio 9:1
So, Kallu have 9x red marbles.
Now the 1st option:
a.Either 9 or 45
∴ 9x = 9 or 45
∴ x = 1 or 5
∴ Kallu having a total of 10x = 10 or 50 marbles
Total marbles with Rekha will be 80 or 40 [80 or 40 both can be divided in ratio 7:1]
Now the 2nd option
b.Either 10 or 50
∴ 9x = 10 or 50
this can't be possible since the value of x isn't natural.
3rd option
c.Either 36 or 72
∴ 9x = 36 or 72
∴ x = 4 or 8
∴ Kallu having a total of 10x = 40 or 80 marbles
So, Rekha having total of 50 or 10 marbles [ 50 or 10 can't be divided into 7:1 ratio]
This option is eliminated.
4th option
d.Either 18 or 36
∴ 9x = 18 or 36
∴ x = 2 or 4
∴ Kallu having a total of 10x = 20 or 40 marbles
And, Rekha will be having a total of 70 or 50 marbles [ Both 70 or 50 can't be divided into ratio 7:1 ]
This option is also eliminated.
∴ Option a) 9 or 45 is the correct one.