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4th Std Scholarship · Intelligence Test

Clock

5 concepts · 40 practice questions with answers · Free to read

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The clock and the angle at a full hour

From daily life

When the school bell rings at 9 o'clock the hands of the clock are at a right angle, and at 6 o'clock they lie in a straight line. We can tell this just by looking at the clock, without measuring. How? The round face of the clock has 12 equal parts.

Simple definition

The clock face is 360° and has 12 numbers. So from one number to the next the gap is 30°. The angle between the hands is the gap between the two hands in degrees.

Angles on the clock

TimeAngle
At 3 o'clock90°
At 6 o'clock180°
At 9 o'clock90°
At 12 o'clock0°
1
Rule 1

The clock has 12 numbers and 360°; so 30° between two numbers.

  • E.g. From 12 to 3 there are 3 numbers. 3 × 30 = 90°.
2
Rule 2

At a full hour the minute hand is on 12 and the hour hand is on that hour's number. Angle = hour × 30.

  • E.g. At 5 o'clock : 5 × 30 = 150°.
3
Rule 3

If the angle comes out more than 180°, subtract it from 360.

  • E.g. At 10 o'clock 10 × 30 = 300°. 360 − 300 = 60°.
4
Rule 4

The angle between the hands is always measured on the smaller side; it is never more than 180°.

  • E.g. At 7 o'clock 7 × 30 = 210°. 360 − 210 = 150°.
Example 1 · easy

What is the angle between the hands at 3 o'clock?

  1. 3 numbers ahead of 12.
  2. 3 × 30 = 90°. Answer : 90°.
Example 2 · medium

What is the angle between the hands at 7 o'clock?

  1. 7 × 30 = 210°. This is more than 180°.
  2. 360 − 210 = 150°. Answer : 150°.
Example 3 · exam type

What is the angle between the hands at 10 o'clock?

  1. 10 × 30 = 300°. This is more than 180°.
  2. 360 − 300 = 60°. Answer : 60°.
Remember

At a full hour angle = hour × 30; if it is more than 180° subtract it from 360.

Common mistake

Writing 210° as the answer at 7 o'clock. The angle between the hands is taken on the smaller side, that is 150°.

Shortcut

Memory clue : "3 o'clock 90, 6 o'clock 180, 9 o'clock 90."

Shortcut

90° at 3, 120° at 4, 150° at 5 : add 30° each hour; after 6 go down again.

Spot the difference

TimeAngle
1 o'clock30°
5 o'clock150°
7 o'clock150°

Practice questions

Easy
  1. 1What is the angle between the hands at 6 o'clock?
  2. 2What is the angle between the hands at 9 o'clock?
  3. 3What is the angle between the hands at 2 o'clock?
Medium
  1. 4What is the angle between the hands at 5 o'clock?
  2. 5What is the angle between the hands at 8 o'clock?
  3. 6What is the angle between the hands at 11 o'clock?
Challenging
  1. 7At which two full hours is the angle 150°?
  2. 8At which full hour are the hands in a straight line?
Show answers (try them yourself first)
  1. 1180° (6 × 30).
  2. 290° (9 × 30 = 270, 360 − 270).
  3. 360° (2 × 30).
  4. 4150° (5 × 30).
  5. 5120° (8 × 30 = 240, 360 − 240).
  6. 630° (11 × 30 = 330, 360 − 330).
  7. 7At 5 o'clock and at 7 o'clock.
  8. 8At 6 o'clock (angle 180°).

How far the minute hand and the hour hand move

From daily life

The minute hand goes a full circle in an hour, but the hour hand moves very slowly. So at 3:30 the hour hand is not on 3, it is between 3 and 4.

Simple definition

The minute hand moves 6° in 1 minute (360° in 60 minutes). The hour hand moves 30° in 1 hour, that is half a degree in 1 minute.

Speed of the hands

HandSpeed
Minute hand6° in 1 minute
Minute hand30° in 5 minutes
Hour hand30° in 1 hour
Hour handHalf a degree in 1 minute
1
Rule 1

Minute hand : minutes × 6.

  • E.g. 20 minutes : 20 × 6 = 120°.
2
Rule 2

Hour hand : hours × 30, plus minutes ÷ 2.

  • E.g. 2 hours 30 minutes : 2 × 30 = 60 and 30 ÷ 2 = 15, total 75°.
3
Rule 3

The minute hand moves 90° in 15 minutes, 180° in 30 minutes, 270° in 45 minutes.

  • E.g. 45 minutes : 45 × 6 = 270°.
4
Rule 4

Thinking backwards : if degrees are given, divide by 6 for the minute hand and by 30 for the hour hand.

  • E.g. The hour hand moved 150° : 150 ÷ 30 = 5 hours.
Example 1 · easy

How many degrees does the minute hand move in 20 minutes?

  1. 6° in 1 minute.
  2. 20 × 6 = 120°. Answer : 120°.
Example 2 · medium

How many degrees does the hour hand move in 2 hours 30 minutes?

  1. In 2 hours 2 × 30 = 60°.
  2. In 30 minutes 30 ÷ 2 = 15°. Total 75°. Answer : 75°.
Example 3 · exam type

How far do the minute hand and the hour hand move in 45 minutes?

  1. Minute hand : 45 × 6 = 270°.
  2. Hour hand : 45 ÷ 2 = 22 and a half, that is 22.5°. Answer : 270° and 22.5°.
Remember

The minute hand moves 6° per minute and the hour hand half a degree per minute; so the minute hand goes 12 times as fast as the hour hand.

Common mistake

Assuming the hour hand does not move with the minutes. At 3:30 the hour hand is not on 3 but at 105°.

Shortcut

Memory clue : "Minute hand 6, hour hand half."

Shortcut

5 minutes = 30°; divide the minutes by 5 and multiply by 30.

Spot the difference

HandIn 1 minuteIn 1 hour
Minute hand6°360°
Hour handHalf a degree30°

Practice questions

Easy
  1. 1How many degrees does the minute hand move in 10 minutes?
  2. 2How many degrees does the minute hand move in 25 minutes?
  3. 3How many degrees does the hour hand move in 2 hours?
Medium
  1. 4How many degrees does the hour hand move in 3 hours 20 minutes?
  2. 5How many degrees does the minute hand move in 1 hour 15 minutes?
  3. 6How many degrees does the hour hand move in 40 minutes?
Challenging
  1. 7The hour hand moved 150°. How much time has passed?
  2. 8The minute hand moved 720°. How much time has passed?
Show answers (try them yourself first)
  1. 160° (10 × 6).
  2. 2150° (25 × 6).
  3. 360° (2 × 30).
  4. 4100° (3 × 30 = 90, plus 20 ÷ 2 = 10).
  5. 5450° (75 minutes × 6).
  6. 620° (40 ÷ 2).
  7. 75 hours (150 ÷ 30).
  8. 82 hours (720 ÷ 360 = 2 rounds, that is 2 hours).

The angle at any time

From daily life

Look at the hands at 3:20. The minute hand is on 4 and the hour hand is a little past 3. They are close. We find the angle between them by finding the position of each hand in degrees.

Simple definition

First find how many degrees each hand is from 12. Then subtract the smaller number from the bigger. If the answer is more than 180°, subtract it from 360.

Steps to find the angle

StepWhat to do
1Hour hand : hours × 30 + minutes ÷ 2
2Minute hand : minutes × 6
3Find the difference of the two
4If it is more than 180°, subtract it from 360
1
Rule 1

Find the position of the hour hand : hours × 30 plus minutes ÷ 2.

  • E.g. At 3:20 3 × 30 = 90 and 20 ÷ 2 = 10, total 100°.
2
Rule 2

Find the position of the minute hand : minutes × 6.

  • E.g. 20 minutes : 20 × 6 = 120°.
3
Rule 3

Subtract the smaller from the bigger.

  • E.g. 120 − 100 = 20°.
4
Rule 4

If the answer is more than 180°, subtract it from 360.

  • E.g. At 10:10 the hour hand is at 305° and the minute hand at 60°; difference 245°. 360 − 245 = 115°.
Example 1 · easy

What is the angle between the hands at 3:20?

  1. Hour hand 100°, minute hand 120°.
  2. Difference 120 − 100 = 20°. Answer : 20°.
Example 2 · medium

What is the angle between the hands at 4:30?

  1. Hour hand 4 × 30 + 15 = 135°. Minute hand 30 × 6 = 180°.
  2. Difference 180 − 135 = 45°. Answer : 45°.
Example 3 · exam type

What is the angle between the hands at 7:10?

  1. Hour hand 7 × 30 + 5 = 215°. Minute hand 10 × 6 = 60°.
  2. Difference 215 − 60 = 155°. Answer : 155°.
Remember

Write the position of both hands in degrees from 12; then take the difference.

Common mistake

Not giving the hour hand its share for the minutes. At 4:30 the hour hand is not at 120°, it is at 135°.

Shortcut

Memory clue : "Hour times 30 plus half the minutes; minutes times 6; difference."

Shortcut

At 6:30 the hour hand is at 195° and the minute hand at 180° : 15°; remember such pairs.

Spot the difference

TimeAngle
3:3075°
6:3015°
9:30105°

Practice questions

Easy
  1. 1What is the angle between the hands at 3:30?
  2. 2What is the angle between the hands at 6:30?
  3. 3What is the angle between the hands at 9:30?
Medium
  1. 4What is the angle between the hands at 2:20?
  2. 5What is the angle between the hands at 5:40?
  3. 6What is the angle between the hands at 8:20?
Challenging
  1. 7What is the angle between the hands at 12:30?
  2. 8What is the angle between the hands at 10:10?
Show answers (try them yourself first)
  1. 175° (hour 105°, minute 180°).
  2. 215° (hour 195°, minute 180°).
  3. 3105° (hour 285°, minute 180°).
  4. 450° (hour 70°, minute 120°).
  5. 570° (hour 170°, minute 240°).
  6. 6130° (hour 250°, minute 120°).
  7. 7165° (hour 15°, minute 180°).
  8. 8115° (hour 305°, minute 60°; difference 245°, 360 − 245).

A clock running fast or slow

From daily life

Grandfather's clock is 10 minutes fast, so he always leaves early. This is the gap between the real time and the clock's time. If the clock is fast, the clock shows more than the real time.

Simple definition

If the clock is fast, clock time = real time + gap. If the clock is slow, clock time = real time − gap. Sometimes a clock gains or loses a few minutes every hour; then multiply the gap by the hours.

Fast and slow clocks

SituationClock time
10 minutes fastReal time + 10 minutes
10 minutes slowReal time − 10 minutes
3 minutes fast every hourHours × 3 minutes gap
1
Rule 1

If fast add, if slow subtract (real time → clock time).

  • E.g. 15 minutes fast; real time 7:00 so the clock shows 7:15.
2
Rule 2

If the clock time is given, do the reverse : find the real time.

  • E.g. 5 minutes fast; the clock shows 5:20 so the real time is 5:15.
3
Rule 3

If the gap is per hour, multiply by the hours passed.

  • E.g. 3 minutes fast per hour; in 8 hours 8 × 3 = 24 minutes.
4
Rule 4

If a clock gains 2 minutes every hour, in 1 real hour it shows 62 minutes.

  • E.g. The clock showed 186 minutes : 186 ÷ 62 = 3 real hours.
Example 1 · easy

The clock is 10 minutes fast. The real time is 4:15. What does the clock show?

  1. It is fast so add.
  2. 4:15 + 10 minutes = 4:25. Answer : 4:25.
Example 2 · medium

The clock is 5 minutes slow. The clock shows 8:40. What is the real time?

  1. It is slow so the real time is more.
  2. 8:40 + 5 minutes = 8:45. Answer : 8:45.
Example 3 · exam type

A clock gains 3 minutes every hour. It was set right at 6:00 in the morning. What does it show when the real time is 2:00 in the afternoon?

  1. 6:00 to 2:00 is 8 hours. Gap 8 × 3 = 24 minutes.
  2. The clock is fast; 2:00 + 24 minutes = 2:24. Answer : 2:24.
Remember

A fast clock shows more than the real time; a slow clock stays behind.

Common mistake

Mixing up fast and slow. If the clock time is given, do the reverse operation to get the real time.

Shortcut

Memory clue : "Fast clock shows more; slow clock shows less."

Shortcut

If the gap is per hour, multiply the number of hours and the gap; that is the total gap.

Spot the difference

SituationClock time when real time is 5:00
10 minutes fast5:10
10 minutes slow4:50
Correct5:00

Practice questions

Easy
  1. 1The clock is 15 minutes fast. The real time is 7:00. What does the clock show?
  2. 2The clock is 10 minutes slow. The real time is 9:30. What does the clock show?
  3. 3The clock is 5 minutes fast. It shows 5:20. What is the real time?
Medium
  1. 4The clock is 4 minutes slow. It shows 11:00. What is the real time?
  2. 5A clock gains 2 minutes every hour. It was set right at 8:00 in the morning. What does it show when the real time is 12:00?
  3. 6A clock loses 3 minutes every hour. It was set right at 6:00 in the morning. What does it show when the real time is 10:00?
Challenging
  1. 7A clock gains 2 minutes every hour. It was set right at 1:00 in the afternoon. It now shows 4:06. What is the real time?
  2. 8A clock loses 4 minutes every hour. It was set right at 9:00 in the morning. It now shows 11:48. What is the real time?
Show answers (try them yourself first)
  1. 17:15 (fast, so add).
  2. 29:20 (slow, so subtract).
  3. 35:15 (the real time is less).
  4. 411:04 (the real time is more).
  5. 512:08 (4 hours × 2 minutes = 8 minutes fast).
  6. 69:48 (4 hours × 3 minutes = 12 minutes slow).
  7. 74:00 (the clock shows 3 hours 6 minutes = 186 minutes; 62 minutes per real hour; 186 ÷ 62 = 3 hours).
  8. 812:00 (the clock shows 2 hours 48 minutes = 168 minutes; 56 minutes per real hour; 168 ÷ 56 = 3 hours).

Mirror time, meetings of the hands and mixed questions

From daily life

If you look at a clock in a mirror, left and right are swapped and the time looks different. In a mirror 3 o'clock looks like 9. The exam also asks how many times the hands meet in a day.

Simple definition

To find the mirror time subtract the real time from 12:00 (treat 12 as 0). The hands lie on top of each other 11 times in 12 hours, in a straight line 11 times and at a right angle 22 times.

Mirror and meetings of the hands

TopicAnswer
Mirror time12:00 − real time
Hands on top of each other (in 12 hours)11 times
In a straight line (in 12 hours)11 times
Right angle (in 12 hours)22 times
1
Rule 1

Mirror time = real time subtracted from 12:00.

  • E.g. Real time 4:20; 12:00 − 4:20 = 7:40.
2
Rule 2

In reverse : if the time seen in the mirror is given, subtracting it from 12:00 gives the real time.

  • E.g. In the mirror 2:50; 12:00 − 2:50 = 9:10.
3
Rule 3

For times like 12:xx treat 12 as 0 : the mirror of 12:30 is 11:30.

  • E.g. 12:00 − 0:30 = 11:30.
4
Rule 4

In 12 hours the hands meet 11 times and lie in a straight line 11 times; in 24 hours 22 times.

  • E.g. A right angle 22 times in 12 hours, 44 times in 24 hours.
Example 1 · easy

The real time is 4:20. What time will show in the mirror?

  1. Subtract 4:20 from 12:00.
  2. 12:00 − 4:20 = 7:40. Answer : 7:40.
Example 2 · medium

The clock in the mirror shows 8:25. What is the real time?

  1. The same operation : 12:00 − 8:25.
  2. 3:35. Answer : 3:35.
Example 3 · exam type

How many times do the hands of a clock lie on top of each other in 12 hours?

  1. In 12 hours the minute hand catches up with the hour hand 11 times.
  2. Answer : 11 times.
Remember

The mirror time and the real time add up to 12:00.

Common mistake

Subtracting from 11:00 instead of 12:00. Subtract from 12:00; for 12:30 the answer is 11:30.

Shortcut

Memory clue : "Mirror = subtract from 12; 11 meetings, 22 right angles."

Shortcut

Subtract hours and minutes separately : for 4:20 take 12 − 4 and then minus 20 minutes, that is 7:40.

Spot the difference

Real timeIn the mirror
3:158:45
6:305:30
9:102:50

Practice questions

Easy
  1. 1The real time is 4:00. What time will show in the mirror?
  2. 2The real time is 3:15. What time will show in the mirror?
  3. 3The real time is 10:20. What time will show in the mirror?
Medium
  1. 4The real time is 7:35. What time will show in the mirror?
  2. 5The mirror shows 2:50. What is the real time?
  3. 6The real time is 12:30. What time will show in the mirror?
Challenging
  1. 7How many times do the hands lie on top of each other in 24 hours?
  2. 8How many times are the hands at a right angle in 12 hours?
Show answers (try them yourself first)
  1. 18:00 (12:00 − 4:00).
  2. 28:45 (12:00 − 3:15).
  3. 31:40 (12:00 − 10:20).
  4. 44:25 (12:00 − 7:35).
  5. 59:10 (12:00 − 2:50).
  6. 611:30 (treat 12:30 as 0:30; 12:00 − 0:30).
  7. 722 times (11 in 12 hours).
  8. 822 times.

Quick revision of the whole lesson

TopicMemory clue
Angle at a full hourHour × 30; if more than 180° subtract from 360
Speed of the handsMinute hand 6, hour hand half
Angle at any timeHour times 30 plus half the minutes; minutes times 6; difference
Fast and slow clockFast shows more; slow shows less
Mirror timeSubtract from 12:00
Meetings of the hands11 times in 12 hours

🎯 Most important points for the exam

  • The clock face has 360° and 30° between two numbers.
  • The minute hand moves 6° in a minute and the hour hand half a degree in a minute.
  • To find the angle, find the position of the hour hand and of the minute hand separately and take the difference.
  • If the angle is more than 180°, subtract it from 360.
  • A fast clock shows more than the real time, a slow clock shows less.
  • Mirror time = 12:00 − real time.
  • In 12 hours the hands lie on top of each other 11 times, in a straight line 11 times and at a right angle 22 times.
🧠 Study mantra

"Hour half, minute six; in the mirror subtract from twelve."