Answer: A At 4 the minutes hand is 4*30 = 120 degree behind the hour hand. The minutes hand takes a lead of 11/2 degree every minute over the hour hand. The time it takes to catch up 120 degree = 120/(11/2) = 240/11 min after 4 This is when they would coincide.
Q. No. 8:
Two clocks show the same time at 4 pm. The first clock loses 10 min every 2 hour and the second gains 10 min every hour. When will they both show the same time again?
Answer: C If they had not lost or gained any time, they would both show the same time always. But in this case, the first clock would be behind the second clock by 15 min at the end of 1 hour. (Since the first clock loses 5 min and the second gains 10 min in 1 hour)They would both show the same time again if they are separated by 12 hr = 12* 60 mins Number of hours the first clock takes to be behind the second by 12 hr => (12*60)/15 = 48 hr So they would show the same time again after exactly 2 days.
Q. No. 9:
The minutes hand of a clock is found to cross the hour hand x minutes past three. Then x= ?
Answer: C At 3'o clock the angle between the hour hand and the minute hand is 90 degree. The minute hand will cover the distance with a relative speed (6 - 0.5) = 5.5 degree per minute. i.e 90/5.5 =
16
4 11
minutes
Q. No. 10:
At what time between 7 and 8 o' clock are the hour and minute hands of a clock together?
Answer: D The hands of a clock are 35 min =(35*6 = 210 degree) apart at 7 o' clock. For the hands to be together, the minutes hand has to gain 210 degree min over the hour hand. Speed of the minute hand relative to the hours hand = 6- (1/2) = 5.5 degree per min. Hence the hands will meet after 210 /5.5
38
2 11
min past 7
Q. No. 11:
The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:
Answer: C Angle traced by hour hand in 13/3 hrs = (360/12 * 13/3) = 130 degree Angle traced by min. hand in 20 min. = (360/60 * 20) = 120 degree Required angle = 130 - 120 = 10 degree.
Q. No. 12:
In a clock having a circular scale of twelve hours, when time changes from 7:45AM to 7:47AM , by how many degrees the angle formed by the hour hand and the minute hand changes?
Answer: B Minute hand cover, 360° in 60 min In 1 min it covers 6° Hours hand cover 1/2 degree in 1 min From 7:45 – 7:47 i.e. after 2 minutes In two minute min. hand moves 6 × 2 = 12° In two minute hr. hand moves 1/2 * 2 = 1 degree Difference required = 12 – 1 = 11°
