# Simple way to solve clock based problems in Aptitude

**Clock problems** are one of the frequently asked questions in most of the competitive exam. To solve these problems, it is always better to understand some of the basic principles and the types of *clock problems* that get asked ,Clock problems are Basically Two Types

In every competitive exam, clock questions are categorized into two ways.

- Problems in angles
- Problems on incorrect clocks

**Problems in angles :**

*Method :1*

Before we actually start solving problems on angles, we need to know couple of basic facts clear:

- Speed of the hour hand = 0.5 degrees per minute
- Speed of the minute hand = 6
- At ‘n’ o’ clock, the angle of the hour hand from the vertical is 30n

*Method :2*

**Angle between X and Y =|(X*30)-((Y*11)/2)|**

angle between hands at 6:30

Step 1: X=6 , Y=30

Step 2: 6*30=180

Step 3: (30*11)/2 = 165

Step 4: 180-165=15

Thus, angle between hands at 6:30 is 15 degrees

**Problems on incorrect clocks:**

*1.**A watch gains 5 seconds in 3 minutes and was set right at 8 AM. What time will it show at 10 PM on the same day?*

The watch gains 5 seconds in 3 minutes = 100 seconds in 1 hour.

From 8 AM to 10 PM on the same day, time passed is 14 hours.

In 14 hours, the watch would have gained 1400 seconds or 23 minutes 20 seconds.

So, when the correct time is 10 PM, the watch would show 10 : 23 : 20 PM

**Important Points:**

- Two right angles per hour(Right angle = 90, Straight angle=180)
- Forty-four right angles per day
- Between every two hours the hands of the clock coincide with each other for one time except between 11, 12 and 12, 1.In a day they coincide for 22 times.
- Between every two hours ,they are perpendicular to each other two times except between 2, 3 and 3, 4 and 8, 9 and 9, 10.In a day they will be perpendicular for 44 times.
- Between every two hours, they will be opposite to each other one time except between 5, 6 and 6, 7.In a day they will be opposite for 22 times.
- When the two hands are at right angles, they are 15-minute spaces apart.
- When the hands are in opposite directions, they are 30-minute spaces apart.
- Angle traced by hour hand in 12 hrs = 360°
- Angle traced by minute hand in 60 min. = 360°.
- If a watch or a clock indicates 10.15, when the correct time is 10, it is said to be 15 minutes
*too fast*.On the other hand, if it indicates 10.45, when the correct time is 10, it is said to be 15 minutes*too slow*