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

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At 4.40 what is the minor angle between the hour hand and the minute  [#permalink]

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New post 29 Jan 2019, 01:24
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

35% (01:37) correct 65% (01:09) wrong based on 25 sessions

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At 4.40 what is the minor angle between the hour hand and the minute  [#permalink]

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New post 29 Jan 2019, 01:38
1
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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Re: At 4.40 what is the minor angle between the hour hand and the minute  [#permalink]

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

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New post 29 Jan 2019, 03:33

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, 03:33
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