Verbal Reasoning - Mental Ability Questions

Your mother's husband — Your father; Your father's sister — Your aunt. 

 So, lady's aunt is man's aunt and therefore lady is man's sister. 

Given number 8, 6, 9, 23, ?

The pattern of given series is:

8 x 1 - 2 = 6 6 x 2 - 3 = 9 9 x3 - 4 = 23 23 x4 - 5 = 87

As shown in fig. the man initially faces in the direction OP. On moving 900 clockwise, he faces in the direction OX. On further moving 1800 anticlockwise, he faces in the direction OY. Finally, on moving 900anticlockwise, he faces in the direction OZ, which is South-east.

Two series alternate here, with every third number following a different pattern.
In the main series, 4 is added to each number to arrive the next.
In alternate series, 5 is subtracted from each number t arrive the next number.
Here in the main series
3 + 4 = 7
7 + 4 = 11
11 + 4 = 15
15 + 4 = 19

In alternate series
24 - 5 = 19
19 - 5 = 14...

The given number series is 200, 200, 100, 300, 75, ?

It follows a pattern that,

200

200 x 1 = 200

200 / 2 = 100

100 x 3 = 300

300 / 4 = 75

75 x 5 = 375

Hence, the next number in the given number sequence is 375.