type 1 angle between the hands of clock Detailed Explanation And More Example

Answer: (c)

∴ Angle traced by hour hand per minute = $(1/2)^o$

&there4 Angle traced by hour hand in 12 h 55 min (i.e., at 0 : 55) = $55 × 1°/2 = 27 1°/2$

&there4 angle traced by minute hand per minute = 6°

Therefore traced by minute hand in 55 min = 55 × 6° = 330°

Therefore required angle = $360° - (330° - 27 1°/2) = 360° + 27 1°/2 - 330°$

$= 387 1°/2 - 330° = 57 1°/2$

Answer: (b)

Angle traced by minute hand per minute = 6°

Therefore angle traced by minute hand in 12 h 20 min = [(2 × 60) + 20] × 6°

= (120 + 20) × 6° = 140 × 6° = 840°

Answer: (d)

∴ angle traced by hour hand per minute = $(1/2)^o$

Therefore angle traced by hour hand in 4 h 10 min = $[(4 × 60) + 10] × 1°/2 = 250 × 1°/2 = 125°$

∴ angle traced by minute hand per minute = 6°

∴ angle traced by minute hand in 10 min = 10 × 6° = 60°

∴ required angle = 125° - 60° = 65°

Answer: (b)

Angle traced by hour hand in $13/3 hrs = (360/12 × 13/3)^o= 130°$

Angle traced by min. hand in $20 min = (360/60 × 20)^o = 120°$

∴ Required angle = (130° - 120°) = 10°

Answer: (d)

Angle traced by the hour hand in $6 hours = (360/12 × 6)^o$ = 180°

Answer: (a)

(A) Angle traced by hour hand in$ 7/6 hrs = (360/12 × 7/6)^o = 35°$

Angle traced by minute hand in $10 min = (360/60 × 10)^o = 60°$

∴ Required angle = (60° - 35°) = 25°

(B) Angle traced by hour hand in $9/4 hrs = (360/12 × 9/4)^o = 67 1°/2$

Angle traced by minute hand in $15 min = (360/60 × 15)^o = 90°$

∴ Required angle = $(90° - 67 1°/2) = 22 1°/2$

(C) Angle traced by hour hand in $26/3 hrs = (360/12 × 26/3)^o = 260°$

Angle traced by minute hand in $40 min = (360/60 × 40)^o$ = 240°

∴ Required angle = (260° - 240°) = 20°