Concepts · Clocks

Mirror time

A clock and its mirror image add up to twelve hours, reading 12 o’clock as 0. Write twelve as 11:60.

Kabir has a clock question in a mock test:

A clock seen in a mirror shows 3:20. What is the real time?

He knows the mirror and the real time make twelve, so he takes each part away: 12 − 3 = 9, and 60 − 20 = 40. 9:40. He ticks it.

The barber’s mirror

On Sunday morning Kabir is in the barber’s chair, facing the big mirror. On the wall behind him is a clock with no numbers, only marks, and in the mirror it reads 3:20. For a second he panics: if it is 3:20 in the afternoon, he has missed cricket practice at noon. Then he twists round. The clock on the wall says 8:40.

He looks from one to the other. 3:20 and 8:40. Three hours twenty and eight hours forty: he adds them, and it is twelve hours exactly. Not 9:40, which is what he wrote in the mock. To take twenty minutes away from twelve o’clock, you first have to write it as 11 hours and 60 minutes; he had taken 3 hours from a whole 12 and forgotten that.

The mirror flips the clock left to right, so each hand sits as far on one side of the 12 as it really is on the other. That is why the two times make twelve hours.

The rule

Real time = 11:60 − mirror time. Take the minutes from 60 and the hours from 11. Read 12 o’clock as 0.

Writing 12:00 as 11:60 does the borrowing before you start, so there is nothing to carry. It works both ways: to find what a mirror will show, take the real time from 11:60 too.

Kabir’s question, again

1. Minutes: 60 − 20 = 40.
2. Hours: 11 − 3 = 8. The real time is 8:40.

9:40, an hour out, is what you get without the borrowing, and it can sit among the options.

Two edges

If the answer comes out at :60, that is the next hour. A mirror showing 3:00 gives 11:60 − 3:00 = 8:60, which is 9:00.

Read 12 o’clock as 0, going in and coming out. A mirror showing 12:30 is 0:30, and 11:60 − 0:30 = 11:30. An answer of 0:15 is 12:15.

This rule is for a clock with hands, in a mirror, which flips left to right. A water image flips top to bottom and follows a different rule, and a digital clock in a mirror is a question about reversed digits.

Why it helps in the paper

Turning a clock round in your head takes several steps. One subtraction from 11:60 gives the answer directly, with the borrowing already done.

The angle between the hands: The clock angle.

Try three

Next mock

A week later, Riya tries him with one:

A clock seen in a mirror shows 10:05. What is the real time?

Kabir writes 11:60 first. 60 − 5 = 55, 11 − 10 = 1. He writes 1:55.