At what angle the hands of a clock are inclined at 15 minutes past 5 ?
At 15 minutes past 5, the minute hand is at 3 and hour hand slightly advanced from 5. Angle between their 3rd and 5th position. Angle through which hour hand shifts in 15 minutes is ∴Required angle =
Question 6 of 24
Find the angle between the hour hand and the minute hand of a clock when the time is 3.25.
Angle traced by the hour hand in 12 hours = 360° Angle traced by it in 3 hrs 25 min. i.e. Angle traced by it in 25 min. Required angle
Question 7 of 24
If a clock strikes 12 in 33 seconds, it will strike 6 in how many seconds?
In order to strike 12, there are 11 intervals of equal time
Therefore, to strike 6 it has 5 equal intervals, it requires 5 × 3 = 15 sec.
Question 8 of 24
At what time between 7 and 8 o’clock will the hands of a clock be in the same straight line but, not together?
When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart. At 7 o’clock, they are 25 min. spaces apart. ∴ Minute hand will have to gain only 5 in. spaces. 55 min. spaces are gained in 60 min. 5 min. spaecs are gained in
Question 9 of 24
At what approximate time between 4 and 5 am will the hands of a clock be at right angle?
Here H × 30 = 4 × 30 = 120°. (Since initially the hour hand is at 4.∴ H = 4). Required angle A = 90° and since, H × 30 > A° so, there will be two timings. Required time T = ²⁄₁₁ (H × 30 ± A) minutes past H. ∴ One timing = ²⁄₁₁ (4 × 30 + 90) minutes past 4. = 38 ²⁄₁₁ minutes past 4. Or 4 : 38 approx.
Question 10 of 24
At what time between 5.30 and 6 will the hands of a clock be at right angles?
At 5 o’clock, the hands are 25 min. spaces apart. To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces 55 min. spaces are gained in 60 min. 40 min. spaces are gained in
Question 11 of 24
At what time between 4 and 5 o’clock will the hands of a watch point in opposite directions?
At 4 o’clock, the hands of the watch are 20 min. spaces apart. To be in opposite directions, they must be 30 min. spaces apart. ∴ Minute hand will have to gain 50 min. spaces 55 min. spaces are gained in 60 min. 50 min. spaces are gained in
Question 12 of 24
At what time between 9’o clock and 10’o clock will the hands of a clock point in the opposite directions?
At 9’o clock, the Minute Hand is ahead of Hour Hand by 15 minutes. The hands will be opposite to each other when there is a space of 30 minutes between them. This will happen when the Minute Hand gains 15 minutes’ space over Hour Hand. Time taken by Minutes Hand to gain 15 minutes
Hence the Hands are opposite to each other at minutes past 9.
Question 13 of 24
At what time between 3 and 4 o’clock, the hands of a clock coincide?
Since, in one hour, two hands of a clock coincide only once, so, there will be value. Required time T = minutes past H. Here H = initial position of hour hand = 3(Since 3 o’clock) A° = required angle = 0°(Since it coincides) T = minutes past 3 = minutes past 3.
Question 14 of 24
Find the exact time between 7 am and 8 am when the two hands of a watch meet ?
55 min spaces are gained in 60 min ⇒35 min spaces will be gained in 38.18 min. ⇒Answer = 7 hrs + 38.18 min.
Question 15 of 24
How much does a watch lose per day, if its hands coincide every 64 minutes?
55 min. spaces are covered in 60 min. 60 min. spaces are covered in Loss in 64 min. Loss in 24 hrs.
Question 16 of 24
An accurate clock shows 8 o’clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 2 o’clock in the afternoon?
Angle traced by the hour hand in 6 hours
Question 17 of 24
A clock is set right at 5 a.m. The clock loses 16 min. in 24 hours. What will be the true time when the clock indicates 10 p.m. on the 4th day ?
Time from 5 a.m. on a day to 10 p.m. on 4th day is 89 hours. Now, 23 hrs. 44 min. of this clock are the same as 24 hours of the correct clock. i.e., ³⁵⁶⁄₁₅ hrs. of this clock = 24 hrs. of correct clock. ∴89 hrs. of this clock =hrs. of correct clock = 90 hrs of correct clock. So, the correct time is 11 p.m.
Question 18 of 24
A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 O’clock, the true time is:
Time from 7 a.m. to quarter pas 4 = 9 hours 15 min.=555 min. Now, 37⁄12 min. of this watch = 3 min. of the correct watch. 555 min. of this watch = min. = of the correct watch. Correct time is 9 hours after 7 a.m. i.e., 4 p.m.
Question 19 of 24
A clock gains 15 minutes per day. It is set right at 12 noon. What time will it show at 4.00 am, the next day?
The clock gains 15 min in 24 hours. Therefore, in 16 hours, it will gain 10 minutes. Hence, the time shown by the clock will be 4.10 am.
Question 20 of 24
A clock is set right at 1 p.m. If it gains one minute in an hour, then what is the true time when the clock indicates 6 p.m. in the same day?
Time interval indicated by incorrect clock = 6 p.m – 1 p.m = 5 hrs. Time gained by incorrect clock in one hour = + 1 min.= + 1/60 hr. Using the formula,
⇒ True time interval ∴ True time = 1 p.m. + hrs. = 5 p.m. + hrs. = 5 p.m. + × 60 min = minutes past 5.
Question 21 of 24
Two clocks were set right at noon on Sunday. One gains 2 min and the other loses 3 min in 24 hours. What will be the true time when the first clock indicates 3 pm on Wednesday?
Time from noon on Sunday to 3 pm on Wednesday = 75 hours. 24 hours 2 minutes of the first clock= 24 hours of the correct one. ⇒ 1 hour of the first clock= 24 × (30/721) hours of correct one. ⇒ 75 hours of the first clock = 24 × 30 × (75/721) hours of correct one = 54000/721 hours = 74 hours 53.7 min. Hence the answer is 2:54 pm.
Question 22 of 24
In a watch, the minute hand crosses the hour hand for the third time exactly after every 3 hrs. 18 min. 15 seconds of watch time. What is the time gained or lost by this watch in one day?
In a watch than is running correct the minute hand should cross the hour hand once in every min. So they should ideally cross 3 times once in min = 196.36 minutes. But in the watch under consideration, they meet after every 3hr, 18 min and 15 seconds, i.e. min. Thus, our watch is actually losing time (as it is slower than the normal watch). Hence when our watch elapsed = 1426.27. Hence the amount of time lost by our watch in one day i.e., 13 min and 50s (approx).
Question 23 of 24
A clock gains 5 minutes. in 24 hours. It was set right at 10 a.m. on Monday. What will be the true time when the clock indicates 10:30 a.m. on the next Sunday ?
Time between 10 a.m. on Mon to 10:30 a.m. on Sun = 144 ½ hrs. 24 ½ hours of incorrect clock = 24 hours of correct time. ∴144 ½ hours of incorrect clock = x hours of correct time. ∴x = = 144 hours i.e., the true time is 10 a.m. on Sunday.
Question 24 of 24
A watch which gains uniformly is 2 minutes slow at noon on Monday and is 4 min. 48 sec. fast at 2 p.m. on the following Monday. When was it correct?
Time from 12 p.m. on Monday to 2 p.m. on the following Monday = 7 days 2 hours = 170 hours. ∴ The watch gains Now, min. are gained in 170 hrs. ∴ 2 min. are gained in ∴ Watch is correct 2 days 2 hrs. after 12 p.m. on Monday i.e. it will be correct at 2 p.m. on Wednesday.