(b) Angle formed by hour hand with 12 O' clock position at 4 : 30 pm = (120° + 15°) = 135° Gain in hour hand in 10 min = (
30
60
)×10 = 5 ∴ Angle formed by hour hand with 12 O’ clock position at 4 : 30 pm =(135°+ 5°) = 140° Angle formed by minute hand with 12 O’ clock position at 4 : 40 pm =(30° x 8) = 240° ∴ Required angle between the hour and minute hands = (240°- 140°) = 100°