RAS Pre 2021, held on 27 October 2021. Question text as printed in RPSC's booklet; answer as per RPSC's final answer key.

When watch shows 7:45 am, the minute hand points towards East. After 3 hours, in which direction does the hour hand point?

Q: What is the answer to RAS Pre 2021 Q115?

(2). Correct — option (2), East - South. The stem does not say which way the watch faces. The working here takes it lying face up, like a map: its hands then turn clockwise in the same sense as North → East → South → West, and directions are measured clockwise from North: East 90°, South-East 135°, South 180°. Step 1 — place both hands at 7:45, measured clockwise from 12. Minute hand at 45 minutes: 45 × 6° = 270° (on the 9) Hour hand: 7 × 30° + 45 × 0.5° = 232.5° The hour hand is 270° − 232.5° = 37.5° anticlockwise of the minute hand. Step 2 — fix the dial to the compass. Minute hand points East = 90° from North. Hour hand = 90° − 37.5° = 52.5° from North Step 3 — move 3 hours on. The hour hand turns 3 × 30° = 90° clockwise. 52.5° + 90° = 142.5° from North Step 4 — name the direction. 142.5° lies between East (90°) and South (180°), 7.5° past South-East: East - South. Check on the dial: the 9 points East, so the 12 points South. At 10:45 the hour hand is between the 10 and the 11, which lie between East and South. The idea to remember: fix the dial to the compass with the hand you know, then turn the hour hand 30° for every hour.

(1)East
(2)East - South
(3)South
(4)North - East

Answer

(2)

Why

Correct — option (2), East - South.

The stem does not say which way the watch faces. The working here takes it lying face up, like a map: its hands then turn clockwise in the same sense as North → East → South → West, and directions are measured clockwise from North: East 90°, South-East 135°, South 180°.

Step 1 — place both hands at 7:45, measured clockwise from 12.
Minute hand at 45 minutes: 45 × 6° = 270° (on the 9)
Hour hand: 7 × 30° + 45 × 0.5° = 232.5°
The hour hand is 270° − 232.5° = 37.5° anticlockwise of the minute hand.

Step 2 — fix the dial to the compass.
Minute hand points East = 90° from North.
Hour hand = 90° − 37.5° = 52.5° from North

Step 3 — move 3 hours on.
The hour hand turns 3 × 30° = 90° clockwise.
52.5° + 90° = 142.5° from North

Step 4 — name the direction.
142.5° lies between East (90°) and South (180°), 7.5° past South-East: East - South.

Check on the dial: the 9 points East, so the 12 points South. At 10:45 the hour hand is between the 10 and the 11, which lie between East and South.

The idea to remember: fix the dial to the compass with the hand you know, then turn the hour hand 30° for every hour.

Why the others are wrong

(1)
East — East is where the minute hand points, both at 7:45 and again at 10:45, since the time is again 45 minutes past the hour.
The stem asks about the hour hand. It turns only 30° an hour, and after 3 hours it stands at 142.5° from North, 52.5° past East.
(3)
South — South is where the 12 on this dial points: the 9 points East, and the 12 is 90° further clockwise.
The hour hand would point South only at 12 o'clock. At 10:45 it is between the 10 and the 11, 37.5° short of the 12, so it points between East and South.
(4)
North - East — North-East is near where the hour hand pointed at the start, 7:45: 52.5° from North, 7.5° past North-East.
The stem asks for its direction after 3 hours. In that time the hour hand turns 90° clockwise, to 142.5°, which is past East and towards South.

Concept

A clock face is 360° divided into 12 hours, so each hour mark is 30° apart. The minute hand moves 6° a minute; the hour hand moves 30° an hour, which is 0.5° a minute.

At h hours and m minutes, measured clockwise from 12: minute hand = 6m degrees, hour hand = 30h + 0.5m degrees.

Compass directions are also measured clockwise, from North: East 90°, South 180°, West 270°, with North-East, South-East, South-West and North-West at 45°, 135°, 225° and 315°.

Once one hand is tied to a compass direction, the whole dial is fixed, and every other position follows by adding or subtracting angles.

RPSC's 2021 syllabus lists "Direction sense test" under Mental Ability in Reasoning & Mental Ability.

Direction sense rests on turning through angles: a right turn is 90° clockwise, a left turn 90° anticlockwise, and a half-turn 180°. A clock adds a steady rate of turning, 30° an hour for the hour hand.

The minute hand gains 6° − 0.5° = 5.5° a minute on the hour hand, the rate behind calculations of the angle between the hands.

Key facts

Minute hand: 6° per minute. Hour hand: 30° per hour, or 0.5° per minute.
At 7:45 the minute hand is 270° from 12 and the hour hand 232.5°, so the hands are 37.5° apart.
Compass bearings run clockwise from North: East 90°, South-East 135°, South 180°.
With the watch face up and the minute hand pointing East at 7:45, the hour hand points 52.5° from North.
Three hours later the hour hand has turned 90° clockwise, to 142.5° from North, between East and South.

Each hand's position on the dial and on the compass

7:45 — minute hand (270° from 12)→East, 90° (given)

7:45 — hour hand (232.5° from 12)→52.5° from North, just past North-East

10:45 — minute hand (270° from 12)→East, 90°

10:45 — hour hand (322.5° from 12)→142.5° from North, between East and South — option (2)

Compass direction = 90° + (dial angle − 270°), both measured clockwise, with the watch lying face up.

Study next

Angle between the hands of a clockCompass bearings and intercardinal directionsTurns through a given angle, clockwise and anticlockwiseDirection of shadows in the morning and eveningMirror images of clocks

Common traps

Answering for the minute hand. At 10:45 the minute hand is back on the 9 and still points East; the stem asks about the hour hand.
Turning the hour hand the wrong way. 90° clockwise from 52.5° gives 142.5°, towards South; 90° anticlockwise would give 322.5°, towards North-West.
Placing the hour hand exactly on the 7 at 7:45. It has moved 45 × 0.5° = 22.5° past the 7.
Reading the dial from underneath. Seen from below, clockwise on the dial runs anticlockwise on the compass, and at 10:45 the hour hand would point 37.5° from North, between North and East; the working here takes the watch lying face up.

A question can tie one hand of a watch to a compass direction and ask where a hand points after some time, as this one does.

A question can also ask for the angle between the hands at a given time, or the direction a person faces after turning through stated angles.

Related PYQs

RPSC_2024_PRE_GS_Q872024Open & attempt →

Mr. X starts walking towards south from point A. After walking 20 m., he reaches at point B. Now he turns left and walks 20 m and reaches at point C. Now he turns 45° anticlockwise, walks a distance 20√3 m and reaches at the point D. What is the shortest distance between point A and point D ?

(1) 20√3 m
(2) 40 m
(3) 20√5 m
(4) 40√3 m

Answer(3)

Same turning of a direction through a stated angle. That question has a walker head south, turn left, then turn 45° anticlockwise, and asks the shortest distance from the start (RPSC's key: 20√5 m); this one turns a watch's hour hand 90° clockwise over 3 hours and asks where it points.

Practice

practice — not a real PYQ
A watch lies face up. At 3:00 its minute hand points towards North. In which direction does the hour hand point?
- (a)East
- (b)West
- (c)South
- (d)North - East
Answer(1) — The minute hand is on the 12, which points North. The hour hand is on the 3, 90° clockwise from the 12, so it points East.
Option (2) turns 90° anticlockwise instead; option (3) is where the 6 points; option (4) is 45° from the 12, where the hour hand points at 1:30.
practice — not a real PYQ
What is the angle between the hour hand and the minute hand of a clock at 7:45?
- (a)37.5°
- (b)45°
- (c)60°
- (d)22.5°
Answer(1) — Minute hand = 45 × 6° = 270°; hour hand = 7 × 30° + 45 × 0.5° = 232.5°; the difference is 37.5°.
Option (2) places the hour hand halfway between 7 and 8; option (3) places it exactly on the 7; option (4) is only how far the hour hand has moved past the 7.