hand on a standard clock

[sanju09]

At 4:40, what is the minor angle between the hour hand and the minute hand on a standard clock?
A. 100
B. 110
C. 120
D. 130
E. 140




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[AIM GMAT]

IMO A . 100

4:40 --- minute hand will be at 8 .

At 4 hour hand will be at 4 , now we need to calculate how many degrees hour hand will move in 40mins.

12 hrs hour hand moves 360 degree
1 hr ---------------------------30 degree
60 min-------------------------30 degree
1 min---------------------------0.5 degree
40min---------------------------20degree

so still 10 degrees are left to cover till hour hand moves to 5 .

Degree between 5 to 8 = 3 * 30 = 90 +10 [left] = 100

[srcc25anu]

(* for degrees)
at 4:00 pm, hour and minute hand are 120 * apart
in 1 minute - hour hand moves 1/2 *
in 1 min minute hand moves 6*

in 40 mins minute hand moves 6 * x 40 = 240*
in 40 mins hour hand moves 0.5 * x 40 = 20*

hour hand moves 20* further of 120* ie its at 140*
minute hand moves 240* from 0* (at 4 o clock)

hence the difference between 2 hands = 240* - 140* = 100*

[HSPA]

ideally 120 ... but the hours hand will be btw 4 and 5 on the 4th minor point

4*6= 24

120-24 = 96

96deg is the minor angle

[sanju09]

(* for degrees)
at 4:00 pm, hour and minute hand are 120 * apart
in 1 minute - hour hand moves 1/2 *
in 1 min minute hand moves 6*

in 40 mins minute hand moves 6 * x 40 = 240*
in 40 mins hour hand moves 0.5 * x 40 = 20*

hour hand moves 20* further of 120* ie its at 140*
minute hand moves 240* from 0* (at 4 o clock)

hence the difference between 2 hands = 240* - 140* = 100*

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