Mental Ability: Directions, Clock Angles, and Mirror/Water Images

Directions and Clock problems regularly appear in Kerala PSC’s Mental Ability section. These are scoring topics if you know the rules. Expect 1-2 questions per paper on directions and 1 question on clocks or mirror images.

Eight Compass Directions

Direction	Abbreviation	Position
North	N	Top
South	S	Bottom
East	E	Right
West	W	Left
North-East	NE	Between N and E (upper-right)
North-West	NW	Between N and W (upper-left)
South-East	SE	Between S and E (lower-right)
South-West	SW	Between S and W (lower-left)

Key Direction Rules

Rule	Details
Facing North, turn right	Now facing East
Facing North, turn left	Now facing West
Facing East, turn right	Now facing South
Facing East, turn left	Now facing North
Opposite of North	South
Opposite of East	West
Opposite of NE	SW
Opposite of NW	SE
Right turn	Clockwise 90 degrees
Left turn	Anti-clockwise 90 degrees
About turn	180 degrees (opposite direction)

Angle Between Directions

Turn	Angle
N to NE (or any adjacent cardinal to intermediate)	45 degrees
N to E (or any cardinal to next cardinal)	90 degrees
N to SE	135 degrees
N to S (opposite)	180 degrees
Full rotation	360 degrees

Direction Problem-Solving Strategy

Step	Action
1	Draw a compass (N-S-E-W) on paper
2	Mark starting position and direction faced
3	For each turn: right = clockwise, left = anti-clockwise
4	Track final position relative to start
5	For distance: use Pythagoras theorem for shortest distance

Common Direction Problem Types

Type	Method
Final direction after turns	Track each turn sequentially on compass
Shortest distance	Draw path, use Pythagoras: d = sqrt(a^2 + b^2)
Direction of B from A	After plotting positions, check relative placement
Shadow-based	Morning shadow falls West (sun in East); Evening shadow falls East (sun in West)

Shadow Direction Rules

Time	Sun Position	Shadow Falls
Morning (sunrise)	East	West
Noon	Overhead (in tropics)	Minimal/directly below
Evening (sunset)	West	East
In India (Northern hemisphere)	Sun is in South at noon	Shadow falls North at noon

Clock Problems

Basic Clock Facts

Fact	Details
Total angle of clock face	360 degrees
12 hours on clock	Each hour = 360/12 = 30 degrees
60 minutes divisions	Each minute = 360/60 = 6 degrees
Hour hand speed	0.5 degrees per minute (30 degrees per hour)
Minute hand speed	6 degrees per minute (360 degrees per hour)
Relative speed	Minute hand gains 5.5 degrees per minute over hour hand
Hands overlap	Every 65 and 5/11 minutes (approximately)
Hands at 180 degrees	Every 65 and 5/11 minutes
Hands at 90 degrees	22 times in 12 hours (not 24, because some coincide)
Hands overlap in 12 hours	11 times
Hands at 180 degrees in 12 hours	11 times

Clock Angle Formula

Angle between hour and minute hand:

Angle = |30H - 5.5M|

Where:

• H = hour (use 12-hour format)
• M = minutes
• If result is above 180, subtract from 360 to get acute/obtuse angle

Examples Using the Formula

Time	Calculation	Angle
3:00		30(3) - 5.5(0)
6:00		30(6) - 5.5(0)
9:00		30(9) - 5.5(0)
12:00		30(12) - 5.5(0)
3:30		30(3) - 5.5(30)
5:20		30(5) - 5.5(20)
7:45		30(7) - 5.5(45)
2:40		30(2) - 5.5(40)

Clock Gain/Loss Problems

Type	Formula
Clock gains x minutes per hour	In t hours, clock shows: actual time + (x times t) minutes
Clock loses x minutes per hour	In t hours, clock shows: actual time - (x times t) minutes
When will both show same time again?	Faulty clock must gain/lose exactly 12 hours (720 minutes) to show same time

Time When Hands Are at Specific Angles

To find time when hands make angle A degrees:

• 30H - 5.5M = A (or) 30H - 5.5M = -A
• Solve for M

Example: At what time after 4 o’clock do hands make 90 degrees?

• 30(4) - 5.5M = 90 then M = (120-90)/5.5 = 30/5.5 = 5 and 5/11 minutes
• 30(4) - 5.5M = -90 then M = (120+90)/5.5 = 210/5.5 = 38 and 2/11 minutes
• Answer: 4:05 and 5/11 minutes OR 4:38 and 2/11 minutes

Mirror Image

Rules for Mirror Images

Rule	Details
Left-right reversal	Mirror placed on left/right side reverses left and right (horizontal flip)
No top-bottom change	Mirror image does not change top and bottom (when mirror is vertical)
Letters/numbers	Appear reversed (R becomes backward R)
Clock in mirror	Shows time as: 11:60 minus actual time (for time between 1:00 and 12:59); simpler: 12:00 minus actual time and adjust

Mirror Image of Clock

To find time shown in mirror:

• Subtract actual time from 11:60 (or 12:00, converting as needed)
• Example: Actual time 3:15 in mirror shows 11:60 - 3:15 = 8:45
• Example: Actual time 8:20 in mirror shows 11:60 - 8:20 = 3:40

Mirror Image of Letters

Original	In Mirror
Symmetric letters (look same)	A, H, I, M, O, T, U, V, W, X, Y
Reverse completely	B, C, D, E, F, G, J, K, L, N, P, Q, R, S, Z
Numbers that look same	0, 8 (vertically symmetric)
AMBULANCE	Written in mirror image on ambulances so it reads correctly in rear-view mirror

Water Image

Rules for Water Images

Rule	Details
Top-bottom reversal	Water image flips upside down (vertical inversion)
No left-right change	Left and right remain the same
Combination	Like looking at reflection in still water — everything flipped vertically

Comparison: Mirror vs Water Image

Feature	Mirror Image	Water Image
Reversal type	Left-Right (horizontal)	Top-Bottom (vertical)
Left becomes	Right	Left (unchanged)
Top becomes	Top (unchanged)	Bottom
Clock reading	11:60 minus actual	Not applicable (upside down)
Used in	Mirrors, ambulance writing	Reflections in water/pools

Quick Recall — PSC Favourites

Question	Answer
Angle between clock hands at 3:00?	90 degrees
Angle at 6:00?	180 degrees
Formula for clock angle?
Hour hand moves per minute?	0.5 degrees
Minute hand moves per minute?	6 degrees
Hands overlap in 12 hours how many times?	11 times
Hands at right angle in 12 hours?	22 times
Mirror image reverses?	Left and Right
Water image reverses?	Top and Bottom
Shadow in morning falls towards?	West
Facing South, turn left means facing?	East
Facing West, turn right means facing?	North
Mirror shows 8:45, actual time?	3:15 (11:60 - 8:45)
AMBULANCE written reversed because?	So it reads correctly in rear-view mirror
Relative speed of minute over hour hand?	5.5 degrees per minute