# Q. The Angle Formed By The Hour hand And Minute hand of a Clock at 2 : 15 p.m. is:

(A) 27.5°

(B) 22.5°

(C) 45°

(D) 30°

Why? Do not worry! Everything is written below from Shortcut Trick to Complete Discription of the Concept and Full Discussion here.

## Shortcut Formula Trick to find The Angle Formed By The Hour hand And Minute hand of a Clock :

It is very easy. Just Remember the formula given below.

To find the angle made by hour hand and minute hand at h : m, where

h = number of hours with respect to 12:00

(example: 7:12 pm means, h = 7

but, 12 : 30 pm means , h = 0 )

m = directly enter the minute.

 Angle = | 11m÷2 – 30h |

Note: If the result is greater than 180° , then substract the result from 360° to get the final result.

## Derivation of The Angle Formed By The Hour hand And Minute hand of a Clock Formula :

We know, A Complete revolution of any hand of a clock = 360°

Now,

Angle made by Minute Hand in 1 Minute

= 360°/60    { 1 revolution = 60 minute}

= 6°

So, Angle made by Minute hand in m minute = 6m°

Angle made by Hour Hand in 1 Minute

= 360°/60×12 { 1 revolution of hour hand = 12 × 60 minute}

= 1/2

Now, at h : m , total minutes = 60 × h + m

= 60h + m

(example: 2:15 means , 60×2 + 15 = 135 minutes)

Angle made by hour hand in (60h + m) minute = (60h + m) × 1/2

= 30h + m/2

So,

Angle between the hour hand and minute hand = 6m – (30h + m/2)

= | 11m÷2 – 30h |

Which is the required formula.

#### Q. Pipes A and B can fill a tank in 8 and 24 hours respectively. Pipe C can empty it in 12 hours. If the three pipes are opened together, then the tank will be fill in

(a) 18 hours

(b) 6 hours

(c) 12 hours

(d) 24 hours

This question is already taken in  SSC GD, UPSC PSC, RRB SSC CHSL CGL MTS , Police Constable and more exams…

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