# how many times are the hands of a clock at right angles in a span of twenty four hours?

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## How many times are the hands of a clock at right angle in a day?

How many times are the hands of a clock at right angle in a day?

Question

How many times are the hands of a clock at right angle in a day?

A 22 B 24 C 44 D 48 Open in App Solution

The correct option is **D** 44

In 12 hours, they are at right angles 22 times.

⇒

In 24 hours, they are at right angles 44 times.

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## [Solved] How many times the hands of a clock are at right angles to r

The minute hand covers 360° in an hour and 6° in a minute. The hour hand covers 30° in an hour and 0.5° in a minute. Calculation: Starting fr

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## Question

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## How many times the hands of a clock are at right angles to reach other in 24 hours?

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22 24 44 48

## Answer (Detailed Solution Below)

Option 3 : 44 Crack with

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## Detailed Solution

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The minute hand covers 360° in an hour and 6° in a minute.

The hour hand covers 30° in an hour and 0.5° in a minute.

**Calculation:**

Starting from midnight i.e. 12 o clock at the midnight, the first time the difference between the two hands would be 90° is:

6x = 0.5x + 90° (x is the number of minutes)

⇒ 5.5x = 90°

⇒ x = 180/11 minutes

The next time the difference between the two hands would be 90° is when the minute hand would have moved 180° away from the hour hand or the difference between both hands would have been 270°.

6x = 0.5x + 270 ⇒ 5.5x = 270

⇒ x = 540/11 minutes

Thus, the difference between two consecutive moments where both hands forms a right angle is:

540/11 - 180/11 = 360/11 minutes

Thus, the two hands form a right angle after every 360/11 minutes.

Total number of minutes in a day = 24 × 60 = 1440 minutes.

Number of times the two hands will form a right angle in a day = 1440 ÷ (360/11)

⇒ (1440 × 11) ÷ 360 ⇒ 4 × 11 = 44 times

Hence, the two hands will form right angle **"44 times"** in a day.

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## More Clock and Calendar Questions

**Q1.**If Rahul claims that the hour hand of his watch makes three-fourth of a revolution in clockwise direction, then where will the hand be if it starts at 5 p.m.?

**Q2.**What is the angle between the minute hand and hour hand when the time shown on the clock is 4 p.m.?

**Q3.**The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:

**Q4.**An accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?

**Q5.**How many times do the hands of a clock coincide in a day?

**Q6.**On 6th March, 2005 Monday falls. What was the day of the week was it on 6th March, 2004 ?

**Q7.**January 1, 2007 was Monday. What day of the week lies on Jan 1, 2008 ?

**Q8.**What was the day of the week on 17th June, 1998 ?

**Q9.**Select the time that would depict the correct mirror image of 4:40 in a clock.

**Q10.**November 17, 2017 falls on Friday. In which of the following years will 17th November fall again on Friday?

## How many times in a 24

Answer (1 of 22): 44 Times; This follows logically from the the following 1) Between one occurrence of the minute and hour hand alining and the next there will be two times that right angles form 2) Between each hour stroke the hands will line up except during the 11:00 to 12:00 period (take 12:0...

How many times in a 24-hour period do the hour and minute hands of a clock form a right angle?

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Muthusamy Piramanayagam ( முத்துசாமி பிரமநாயகம்)

Head of department of Physics . Technical Education .Tamil Nad, iIndiaAuthor has 7.2K answers and 5.4M answer views3y

Angular speed of hour hand is 0.5°/minute.

Angular speed of minute hand is 6 ° / minute.

Relative to hour hand , the angular speed of minute hand is 5.5 ° per minute.

The hour hand stops rotating , minute hand moves slower than before)

At 12 O clock, the angle is zero.

90/ 5.5 gives 16.3636363636 minutes

There are 1440 minutes in 24 hour .

1440/ 16.36 is 88 ( rounded)

This is for the 4 quadrants .

But we have to consider only 2 quadrants.

Therefore the answer is 88/ 2 = 44

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Andrew Green

Works at Automated LogicAuthor has 57 answers and 72K answer views7y

44 Times; This follows logically from the the following

1) Between one occurrence of the minute and hour hand alining and the next there will be two times that right angles form

2) Between each hour stroke the hands will line up except during the 11:00 to 12:00 period (take 12:00 alinement to be included 12:00 to 1:00)

3) In each 12 hour period there are 11 alinements - take two 12 hour periods and two right angles per alignment to find 11⋅2⋅2 = 44

We can also use mathematics to find the number of alinements

take x to be the absolute number of minutes passed (0 to 24⋅60)

take m as minute hand p

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Related

How many right angles are in 24 hours?

44.

English explanation: (if you want a math explanation look at the last paragraph)

At first you might think 2 per hour which means 48, but that isn’t the case. The thing is, when the minute hand moves, so does the hour hand. It shifts a little, causing the time in the hour that forms a 90 degree angle to be different everytime.

When putting that into consideration, we can find that it forms a 90 degree angle (90 and 270) once every 1964 seconds, which is around 33 minutes. That extra 3 minutes stacks up and eventually causes 1 hour to only be able to form one 90 degree angle. This happens 4 tim

Loring Chien

I took this geometry/Trig stuff over 50 years ago.It hasn't changed a bit.Author has 55.6K answers and 136.3M answer viewsUpdated 4y

Those who said 44 are right. Those who said 48 are close but wrong.

Here's the intuitive solution:

At first blush it would seem intuitively that 48 is right... each 12 hours it happens twice, once at 15 after and once at a quarter till, times two for the twenty four hour = 48. But that solution has one fault, that as the hours progress, the minute hand lines up 90 degrees later in in the hour. for example the 3:xx alignment at 90 deg happens around 3:33 because the hour hand is already past 90 degrees on the clock face so the minute hand is past the "6". In fact exactly 9:00 the minute hand laps

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How many times are the hands of the clock at the right angle in a day?

How many times in 24 hours the hands of a clock will be at straight angles?

Deven Yuvraj

I am still learning the ways to improve my english.6y

Since a clock makes two 2 right angles between any two hours .

PS: right angles are formed when distance between minute hand and hour hand is equal to 15 minutes

so in 12 hours pairs during day and 12 hours pair during night

so answer should be equal to 24*2 =48

BUT two situations

2–4(day and night pair) and

8–10 (day and night pair)

PS : YOU CAN CALCULATE IF YOU WANT HOW MANY RIGHT ANGLES BETWEEN 2–4 AND 8–10 BY FORMULA (30H-5.5M) =90 OR -90 OR 270 OR -270

NOTE: you will get total 1 right angles between 2–3 and using formula you will get total 3 right angles

ANSWER:

24 pairs- 8 pairs =16 pairs so 16*2

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Related

How often in 24 hours do the hour and minute hands of a clock form a right angle?

48

In every hour the minute and hour hand makes right angle for two times

Guys, does anyone know the answer?