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At 4.40 what is the minor angle between the hour hand and the minute

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Math Expert
Joined: 02 Sep 2009
Posts: 53061
At 4.40 what is the minor angle between the hour hand and the minute  [#permalink]

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29 Jan 2019, 00:24
00:00

Difficulty:

55% (hard)

Question Stats:

31% (01:37) correct 69% (01:13) wrong based on 21 sessions

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At 4.40 what is the minor angle between the hour hand and the minute hand.

(A) 100
(B) 110
(C) 120
(D) 130
(E) 150

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Director
Joined: 18 Jul 2018
Posts: 675
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
At 4.40 what is the minor angle between the hour hand and the minute  [#permalink]

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29 Jan 2019, 00:38
The formula to calculate the angle between the hour hand and the minute hand is given by

ϴ (Theta or Angle) = $$|\frac{11}{2}*M - 30*H|$$ = $$|\frac{11}{2}*40-30*4|$$ = |220-120| = 100

M is minutes and H is hours.

A is the answer.
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Joined: 18 Aug 2017
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Re: At 4.40 what is the minor angle between the hour hand and the minute  [#permalink]

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29 Jan 2019, 01:29
Bunuel wrote:
At 4.40 what is the minor angle between the hour hand and the minute hand.

(A) 100
(B) 110
(C) 120
(D) 130
(E) 150

use formula :
11* min/2 - 30* hr

11*40/2- 30*4
= 100
IMO A
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Joined: 04 Jan 2015
Posts: 2589
Re: At 4.40 what is the minor angle between the hour hand and the minute  [#permalink]

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29 Jan 2019, 02:33

Solution

To find:
• The minor angle between the hour hand and the minute hand at 4:40

Approach and Working:
At 4:40,
• The minute hand will exactly be on 8, and
• The hour hand lies between 4 and 5

Let’s find the angle, when the hours hand is on 4 and the minutes hand is on 8
• Angle between any two consecutive digits in a clock = $$\frac{360}{12} = 30$$
• Thus, the angle between 4 and 8 = 4 * 30 = 120 degrees

From this, we need to subtract the angle covered by hours hand in 40 minutes after 4.
• Hours hand covers 30 degrees in 1 hour or 60 minutes
• Thus, it covers $$30 * \frac{40}{60} = 20$$ degrees in 40 minutes

Therefore, the angle between hours and minutes hand at 4:40 = 120 – 20 = 100 degrees

Hence, the correct answer is Option A

Answer: A

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Re: At 4.40 what is the minor angle between the hour hand and the minute   [#permalink] 29 Jan 2019, 02:33
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