# Problems on Clocks: Important for Competitive Exams

I hope that you have solved all the homework questions that I’ve given in the last article. If you still find it difficult to solve please comment your doubts in the section below. Today I am going to tell you a very important topic that is ‘Clock’. I personally feel that clock is a very important, interesting and easy topic. So guys will really enjoy learning this topic. So let us start with topic.

**Basic Concept: **

A clock has two hands, the smaller one is called the hour hand or short hand while the larger one is called the minute hand or long hand.

(i) In 60 minutes the minute hand gains 55 minutes on the hour hand.

(ii) In every hour both the hands coincide once.

(iii) The hands are in the same straight line when they are coincident or opposite each other.

(iv) When two hands are at right angles, they are 15 minutes space apart.

(v) Angle traced by hour hand is 12 hrs = 360 degrees

(vi) Angle traced by minute hand in 60 mins = 360 degrees

Interchange of Hands: Whenever the hands of the clock interchange positions, the sum of the angles traced by hour hand and minute hand is 360 degrees.

**Solved Examples:**

**1. At what time between 2 and 3 o’clock will the hands of a clock be together?**

Solution: At 2 o’clock, the hour hand is at 2 and the minute hand is at 12, that is they are 10 min. spaces apart.

To be together, the minute hand must gain 10 minutes over the hour hand.

Now, 55 minutes are gained by it in 60 min.

Therefore 10 minutes will be gained in (60/55 * 10)min. = 10 * 10/11 min

Therefore the hands will coincide at 10 * 10/11 min. past 2.

**2. Find at what time between 8 and 9 o’clock will be the hands of a clock be in the same straight line but not together.**

Solution: At 8 o’clock, the hour hand is at 8 and the minute hand is at 12 that is the two hands are 20 min. spaces apart.

To be in the same straight line but not together they will be 30 minutes spaces apart.

So the minute hand will have to gain (30 – 20) = 10 minutes spaces over the hour hand.

55 minute spaces are gained in 60 min.

10 minutes spaces will be gained in (60/55 * 10) min. = 10 * 10/11 min

Therefore hands will be in the same straight line but not together at 10 * 10/11 min. past 8.

**3. At what time between 5 and 6 o’clock are the hands of a clock 3 minutes apart?**

Solution: At 5 o’clock, the minute hand is 25 min. spaces behind the hour hand.

Case 1: Minute hand is 3 min. spaces behind the hour hand.

In this case, the minute hand has to gain (25 – 3) = 22 minutes spaces.

55 min. are gained in 60 min.

22 min. are gained in (60/55 * 22) min. = 24 min.

Therefore the hands will be 3 min. apart at 24 min. past 5.

Case 2: Minute hand is 3 min. spaces ahead of the hour hand.

In this case, the minute hand has to gain (25 + 3) = 28 min. spaces.

55 min. are gained in 60 min.

28 min. are gained in (60/55 * 28) min. = 31 * 5/11 min.

Therefore the hands will be 3 min. apart at 31 * 5/11 min. past 5.

**Homework Questions:-**

**1. London time is five and a half hours behind Delhi time. What time is it in London if it is 0.2.35 in Delhi?**

a. 07.05 b. 08.05 c. 21.05 d. 21.35

**2. A bus leaves at 12.25 noon and reaches destination at 10.45 am. The duration of the journey is**

a. 22 hrs 20 min b. 22 hrs 40 min c.24 hrs 20 min d. 24 hrs 40 min

**3. How many rotations will the hour hand of a clock complete in 72 hours? (Bank recruitment exams, 2006)**

a. 3 b. 6 c. 9 d. 12

**4. At 9.38 A.M, through how many degrees the hour hand of a clock moved since noon the previous day?**

a. 323 b. 612 c. 646 d. 649

**5. An accurate clock shows the time as 3.00. After the hour hand has moved 135 degree, the time would be**

a. 6.30 b. 7.30 c. 8.00 d. 9.30

Please do solve the above questions it will only enhance your ability to solve objective type questions. For more information please visit https://www.eckovation.com/ and do subscribe to http://banking.eckovation.com/ if you want to crack competitive exams. Thank you. All the best.

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