RRB NTPC - Clocks and Time

1.

How much does a watch lose per day, if its hands coincide every 64 minutes? 

   A.) 32 8/11min
   B.) 36 5/11min
   C.) 90min
   D.) 96min

Answer: Option 'A'

55 min. spaces are covered in 60 min.
60 min spaces are covered in (60/55 × 60)min = 65 5/11 min
Loss in 64 min = ( 65 5/11- 64 ) = 16/11 min
Loss in 24 hrs = ( 16/11 × 1/64 × 24 × 60 ) min
= 32 8/11 min

2.

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? 

   A.) 144º
   B.) 150º
   C.) 168º
   D.) 180º

Answer: Option 'D'

Angle traced by the hour hand in 6 hours = ( 360/12 × 11/3 )degrees 
=180º

3.

How many times do the hands of a clock coincide in a day? 

   A.) 20
   B.) 21
   C.) 22
   D.) 23

Answer: Option 'C'

The hands of a clock coincide 11 times in every 12 hours 
(Since between 11 and 1, they coincide only once, 
i.e. at 12 o'clock). 
==> The hands coincide 22 times in a day.

4.

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

   A.) 10.30pm
   B.) 11pm
   C.) 10.45pm
   D.) 11.15pm

Answer: Option 'B'

Time from 5am. On a day to 10pm. on 4th day = 89 hours. 
Now 23 hrs 44 min. of this clock = 24 hours of correct clock 
365/15 hrs of this clock = 24 hours of correct clock 
89 hrs of this clock = ( 24 × 15/356 × 89) hrs of correct clock
= 90 hrs of correct clock. 
So, the correct time is 11pm. 

5.

At what time between 5.30 & 6 will the hands of a watch be at right angle? 

   A.) 43 7/11 min past 5
   B.) 41 2/11 min past 5
   C.) 42 min past 5
   D.) 44 1/11 min past 5

Answer: Option 'A'

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 55min. spaces are gained in 60min.
4min. spaces are gained in (60/55 × 40) min. = 43 7/11min. 
Required time = 43 7/11min.past 5.