Exams

Let the total length of the pencil = x cms

From the given data,

'x/8' is black

Remaining part = x - x/8 = 7x/8

1/2 of 7x/8 is white

=> 7x/16 is white (Remaining part is 7x/16)

And given that the remaining part is blue and is 3 1/2 cm = 7/2 = 3.5 cm

That remaining part = 7x/16

Therefore,

7x/16 = 7/2

x = 16/2 = 8

Hence, the total length of the pencil = x = 8 cm.

We know that the day repeats every 7 days, 14 days, 21 days,...

So if today is Monday, after 7 days it is again Monday, after 14 days again it is Monday.

Hence, after 2 weeks i.e, 14 days the day repeats and is the same day. 

Fish is from eggs whereas plant is from seeds.

Total days from 25th June to 15th August = 5 + 31 + 15 = 51 days

51/7  = 7 weeks and 2 days 

August 15 = Wednesday + 2 = Friday

We know that

Sum of Interior angles of Polygon = 180(n-2)
Sum of Exterior angles of Polygon = 360
so 180(n-2)=2x360
Therefore, by solving we get n=6 sides.

The puzzle's logic is

1st figure : (9-7) + (8-5) = 2 + 3 = 5

2nd figure : (15-6) + (11-2) = 9 + 9 = 18

similarly, 3rd figure : (9-6) + (17-5) = 3 + 12 = 15.