# What time is clock showing?

Keval a cool and very very Intelligent boy. One day he was given a clock by Hemil as shown in figure.

It has no numbers, and it may have been rotated out of position.

Also, the second hand, minute hand, and hour hand had the same length.

But it was known that it operated like a standard timepiece.

Keval quickly replied the time and it was correct.

What time was it?

Fun Fact: Such questions are given to 13-14 year olds in Russia.

Hint: Check the position of hand and try to figure it out.

It has no numbers, and it may have been rotated out of position.

Also, the second hand, minute hand, and hour hand had the same length.

But it was known that it operated like a standard timepiece.

Keval quickly replied the time and it was correct.

What time was it?

Fun Fact: Such questions are given to 13-14 year olds in Russia.

Hint: Check the position of hand and try to figure it out.

Answer : 4:50

Explanation:

Hand A and B are pointing to numbers(Major marking).

lets think if hour hand is on any number(Major Marking), minute hand and second hand must be overlapping on 12. But that's not the case as all three hands are positioned different.

So, we can conclude that C is hour hand. And A or B must be second hand and minute hand.

If, minute hand is on any number(Major Marking), then second hand must be on number 12.

From this we can conclude that one of A or B is pointing number 12.

But we don't know which one therefore, we have 2 cases.

CASE: 1

B is second hand

A is minute hand

Let's number all major Major marking(i.e. B is pointing number 12 and A at 2 and C is between 6 and 7).

In this case time is 6:10

But there is one the problem. If it is 6:10 then hour hand which is C must be near to 6 as 10 minutes means 1/6 of the way between 6 and 7.

CASE 1 failed.

CASE: 2

A is second hand

B is minute hand

Let's number all major Major marking. A is 12, C is slightly behind 5 and B is on 10.

According to this, time is 4:50.

Also the hour hand is slightly behind 5, this situation fits perfectly.

Hence, 4:50 is the correct time.

This is how Keval solved the problem.

Explanation:

Hand A and B are pointing to numbers(Major marking).

lets think if hour hand is on any number(Major Marking), minute hand and second hand must be overlapping on 12. But that's not the case as all three hands are positioned different.

So, we can conclude that C is hour hand. And A or B must be second hand and minute hand.

If, minute hand is on any number(Major Marking), then second hand must be on number 12.

From this we can conclude that one of A or B is pointing number 12.

But we don't know which one therefore, we have 2 cases.

CASE: 1

B is second hand

A is minute hand

Let's number all major Major marking(i.e. B is pointing number 12 and A at 2 and C is between 6 and 7).

In this case time is 6:10

But there is one the problem. If it is 6:10 then hour hand which is C must be near to 6 as 10 minutes means 1/6 of the way between 6 and 7.

CASE 1 failed.

CASE: 2

A is second hand

B is minute hand

Let's number all major Major marking. A is 12, C is slightly behind 5 and B is on 10.

According to this, time is 4:50.

Also the hour hand is slightly behind 5, this situation fits perfectly.

Hence, 4:50 is the correct time.

This is how Keval solved the problem.