Sangeeta and Swati bought two wristwatches from Jamshedpur Electronics at 11.40 A.M. IST. After purchasing they found that when 60 minutes elapses on a correct clock (IST), Sangeeta’s wrist watch registers 62 minutes whereas Swati’s wristwatch registers 56 minutes. Later in the day Sangeeta’s wristwatch reads 10 P.M., then the time on Swati’s wristwatch is:

Answer: B As per the data in the question when Sangeeta’s wrist-watch moves 62 minutes Swati’s wrist-watch moves only 56 minutes. =>When Sangeeta’s wrist-watch will move 620 minutes, Swati’s wrist-watch will move only 560 minutes. So there will be a difference of 60 minutes between the times shown by the wrist-watches of Sangeeta and Swati. =>If Sangeeta’s wrist-watch shows 10 p.m. Swati’s wrist watch will show 9 p.m.

Q. No. 2:

A watch, which gains uniformly, is 2 min slow at noon on monday, and in 4min,48 sec fast at 2 pm on the following monday. What time it was correct?

Answer: B Time from monday noon(12 pm) to 2 pm the following monday => 7 days 2 hour = 170 hr Now, the watch gains (2+ 24/5) min from monday So, the watch gains 34/5 min in 170 hours. Therefore, it will gain 2 min in 50 hr = 2 days 2 hour. Therefore the watch is correct after 2 days 2 hour from monday noon or at 2 pm on wednesday.

Q. No. 3:

A clock is set right at 5 am. The clock loses 16 min in 24 hours. What will be the right time when the clock indicates 10pm on the 4th day?

Answer: B Time from 5 am of a particular day to 10pm on the 4th day is 89hr. Now clock loses 16min in 24 hr or in other words we can say that 23 hr 44 min of this clock is equal to 24hr of the correct clock. or (23 + 44/60) => 365/15 hr of this clock = 24 hr of the correct clock. 89 hr of this clock = {(24*15)/356}* 89 hr = 90 hr of the correct clock. or 89 hours of this clock = 90 hr of the correct clock Therefore, it is clear that 89 hr this clock loses 1 hr and hence correct time is 11pm, when the clock shows 10pm.

Q. No. 4:

A clock gaining 2 min every hour was synchronised at midnight with a clock losing 1 min every hour. How many minutes the clock (losing time)will be behind at eleven in the following morning?

Answer: D Suppose both the clocks at 12pm. In the following morning 11 am, the gaining clock is 22 min ahead and losing clock is 11 min behind from the real time. The clock losing the time is 33 min behind the clock gaining the time.

Q. No. 5:

At what angle the hands of a clock are inclined at 15 minutes pasts?

Answer: B At 15 min past 5, the minutes hand is at 3 and hour hand slightly ahead of 5. Now, the angle through which hour hand shifts in 15 min = (15 * 1/2) = 7.5 degree Angle at 15 min past 5 = 60 + 7.5 = 67.5^{o}

Q. No. 6:

A man on his way to dinner shortly after 6:00 pm observes that the hands of his watch from an angle 110 degree. Returning before 7:00 om, he notices that again the hands of his watch form an angle 110 degree. the number of minutes that he has been away is

Answer: B Let after 6:00 pm and m seconds the hands of his watch form an angle of 110 degree for the first time and after 6:00 pm and n seconds the hands of his watch form an angle 110 degree for the second time. In every one second the minutes hand covers 360/3600 = 1/10 degree In every one second the hour's hand covers 30/3600 = 1/120 degree (This is because the minute's hand covers one circle or 360 degree in one hour or 3600 seconds while hour's hand covers 1/12 th of a circle or 30 degree in one hour or 3600 seconds). Initial angle formed at 6:00 pm = 180 degree. Angle formed by the hands of his watch => 180 + m/120 - m/10 when minutes hand behind the hour hand. and, n/10 - n/120 -180 when hours hand is behind the minutes hand. So, 180 - 11m/120 = 110 or 11m/120 = 70............(i) => and 11n/120 - 180 = 110 => 11n/120 = 290.....(ii) Equation(ii) - Equation(i) => m - n = 2400 seconds = 40 minutes.