AFCAT Numerical Ability · Clock

Mirror Images of a Clock

A mirror standing beside a clock swaps left and right, so the image time is 11:60 minus the real time, and the same subtraction takes an image back to the real time.

All Clock notes

Why this matters

Every question here is one subtraction from 11:60, and it works in both directions. The marks go at the edges: times after 11 o'clock that come out as 0 hours, and questions that move the clock on before or after the reflection.

Concept 1 of 3: The image time is 11:60 minus the real time

A plane mirror flips the dial across the line from 12 to 6. A hand that points some distance round from 12 on the right of the dial appears the same distance round from 12 on the left, so the real time and the image time always add up to 12 hours.

Definition

Image time $= 11{:}60 -$ real time. Writing 12:00 as 11:60 lets you subtract without borrowing.
Check: real time plus image time is always 12:00.
On the hour: $11{:}60 - 2{:}00 = 9{:}60$ , which is written 10:00.
6:00 and 12:00 look the same in the mirror.

Mirror time

\text{image} = 11{:}60 - \text{real time}

Worked example

A clock shows 3:25. What time does its mirror image show?

Practice this conceptself-check · 3 quick reps

The same idea in a practice question:

Practice questionModerate

Example 1 · Clock · Mirror Images

The actual time is

9:10

. What will be the corresponding mirror image time on a 12‑hour wall clock?

Subtract from 11:60, not 12:00

Subtracting 2:40 from 12:00 digit by digit tempts you to 10:20. With 11:60 there is nothing to borrow:

11{:}60 - 2{:}40 = 9{:}20

60 minutes is the next hour

11{:}60 - 5{:}00 = 6{:}60

, which a clock shows as 7:00. Writing 6:60 as the answer matches no option.

Drill 7 more on the image time is 11:60 minus the real time

Concept 2 of 3: Finding the real time from the image

Reflecting twice gives back the original, so the rule runs both ways. Subtract the image time from 11:60 and you have the real time.

Definition

Real time $= 11{:}60 -$ image time.
The same check: real plus image is 12:00.
'The reflection shows', 'seen in a mirror' and 'the image appears as' all give the image; the answer asked is the real time.

Real time from the image

\text{real} = 11{:}60 - \text{image}

Worked example

A clock seen in a mirror appears to show 2:35. What is the real time?

Practice this conceptself-check · 3 quick reps

The same idea in a practice question:

Practice questionModerate

Example 2 · Clock · Mirror Images

The reflection of a clock indicates

3:40

. What is the actual time on the 12‑hour analog clock?

The image is not 6 hours off

An image of 1:20 is not 7:20 in real time. Only 12:00 minus the image works:

11{:}60 - 1{:}20 = 10{:}40

Drill 5 more on finding the real time from the image

Concept 3 of 3: Times after 11, time passing and other twists

The rule stays the same; the work is around it. After 11 o'clock the subtraction gives 0 hours, which a dial shows as 12. When time passes, move the real clock, never the image.

Definition

A result of $0{:}m$ is read as $12{:}m$ . A time of $12{:}m$ is read as $0{:}m$ before subtracting.
Time passing: find the real time first, add or subtract the time passed, then reflect again only if the image is asked.
A real time between $h$ and $h + 1$ has its image between $11 - h$ and $12 - h$ , so a time and its image are never in the same hour, except at exactly 6:00 and 12:00.
A 24-hour version of the rule subtracts from 23:60 instead of 11:60.

Reading 0 hours

11{:}60 - 11{:}m = 0{:}(60 - m) = 12{:}(60 - m)

Worked example

A clock shows 11:20. What does its mirror image show? If an image shows 12:20, what is the real time?

Practice this conceptself-check · 3 quick reps

The same idea in a practice question:

Practice questionHard

Example 3 · Clock · Mirror Images

Two and a quarter hours back, the mirror image of a wall clock (12‑hour dial) seemed to show

1:30

. What is the current actual time on the clock?

Move the real clock, not the image

Two hours ago the image showed 3:10, so the real time then was 8:50 and now it is 10:50. Adding the two hours to the image first gives 5:10, whose reflection is 6:50: wrong, because the image runs backwards.

There is no 0 on the dial

11{:}60 - 11{:}50

is 0:10, which a 12-hour dial shows as 12:10.

Drill 5 more on times after 11, time passing and other twists

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (3)

The image time is 11:60 minus the real time
Mirror time
$\text{image} = 11{:}60 - \text{real time}$
Finding the real time from the image
Real time from the image
$\text{real} = 11{:}60 - \text{image}$
Times after 11, time passing and other twists
Reading 0 hours
$11{:}60 - 11{:}m = 0{:}(60 - m) = 12{:}(60 - m)$

Watch out for (5)

Subtract from 11:60, not 12:00
→ The image time is 11:60 minus the real time
60 minutes is the next hour
→ The image time is 11:60 minus the real time
The image is not 6 hours off
→ Finding the real time from the image
Move the real clock, not the image
→ Times after 11, time passing and other twists
There is no 0 on the dial
→ Times after 11, time passing and other twists

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