Dear Reader, Below are three sample problems dealing with time gain/loss by minute and hour hands of clocks.

Question 1

Priya was presented with new brand watch, as marriage anniversary gift by her husband. She observed, that the two hands of the new watch coincide every 64 minutes. She was trying to calculate, how many minutes the watch will lose per day. Can you guide Priya?

(a)32 8/11 (b)36 5/11 (c) 90 minutes (d) 96 minutes

Answer : a)32 8/11

Solution:

55 min spaces are gained by minute hand (with respect to hour hand) in 60 min. (In 60 minutes, hour hand will move 5 spaces while the minute hand will move 60 spaces. In effect the space gain of minute hand with respect to hour hand will be 60 - 5 = 55 minutes.)

In 60 min it will gain ,
60/55 x60 =65 5/11 min.

But minute hand of Priya's watch gains only 64 minutes (it is slow than normal)
Actual loss=65 5/11 -64 =1 5/11 = 16/11min

In 64 min. the loss is 16/11 min
In 24 hours the loss is = (16/11 x1/64 x24 x60)min =32 8/11 minutes.

Question 2

It was 4’o clock in the evening. Shilu was staring at the new watch that was presented by her Dad two day's ago. She was trying to measure the exact time between 4 and 5’o clock during which the hands of the watch point in opposite directions forming a straight line. What would be that time?

(a) 45 minutes past 4 (b)40 minutes past 4 (c) 50 4/11 minutes past 4
(d)54 6/11 minutes past 4.

Answer : d)54 6/11 minutes past 4.

Solution:

At 4’o clock the hands are 20 minutes apart.To form a straight line in opposite direction the hands must be in 30 minutes apart. To accomplish this the minute hand have to close up the 20 minutes separation and after crossing the hour hand it has to gain 30 minute separation. In total minute hand will have to gain 20 + 30 = 50 minutes spaces apart.

55 min spaces are gained in 60 min. (In 60 minutes, hour hand will move 5 spaces while the minute hand will move 60 spaces. In effect the space gain of minute hand with respect to hour hand will be 60 - 5 = 55 minutes.)

50 min spaces can be gained in 60/55 x50 = 54 6/11 minutes.
Hence the answer is 54 6/11 minutes past 4

Question 3

The famous church in the city of Kumbakonnam has a big clock tower and is said to be over 300 years old. Every Monday 10.00 A M the clock is set by Antony, doing service in the church. The Clock loses 6 mins every hour. What will be the actual time when the faulty clock shows 3 P.M on Friday?

(a) 4 A.M (b) 3.16 P.M. (c) 4.54 A.M. (d) 3 A.M

Answer : c) 4.54 A.M

Solution:

Total hours from Monday 10.00 AM to Friday 3.00 PM =101 HOURS

The clock loses 6 minutes every hour. In 101 hours it will lose 101 x 6 =606 minutes. ie 10 hours 06 minutes.

To find the actual time, calculate 10 hours 6 min backwards from Friday 3.00 PM which is 4 .54 AM

Hence the actual time would be 4 .54 AM when clock shows 3.00 PM on Friday.