1. A clock is started at noon. By 10 minutes past 5, the hour hand has turned through:

**Answer: **155º

**Explanation:**
Angle traced by hour hand in 12 hrs. = 360°

Angle traced by hour hand in 5 hrs 10 min.

=> 31/6 hrs = (360/12 * 31/6)º = 155º.

2. Fifty minutes ago it was four times as many minutes past three o'clock. How many minutes is it to six o'clock..?

**Answer: **26 min

**Explanation:**
There are 180 minutes between 3 o'clock and 6 o'clock.

Call x the number of minutes to 6 o'clock.

Then it is 180 - x minutes past 3 o'clock and 50 minutes ago it was 130 - x minuted past 3 o'clock.

Using the 4 times as many minutes past three o'clock bit we can form the equation

130 - x = 4x and solve it

130 = 5x

x = 26 so yes it is 26 minutes.

3. How many times in a day, are the hands of a clock in straight line but opposite in direction?

**Answer: **22

**Explanation:**
The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clock only).

So, in a day, the hands point in the opposite directions 22 times.

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?

**Answer: **11pm

**Explanation:**
Total Time from 5 am. On a day to 10pm. on 4th day = 89 hours.

=> 23 hrs 44 min. of this clock = 24 hours of correct clock

=> 365/15 hrs of this clock = 24 hours of correct clock

=> 1 hrs of this clock = (24 * 15/356) hrs. of correct clock.

so, 89 hrs of this clock = ( 24 * 15/356 * 89) hrs of correct clock = 90 hrs of correct clock.

So, correct time is 11pm.

5. An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?

**Answer: **180º

**Explanation:**
Angle traced by the hour hand in 6 hours = (360/12 * 6)º = 180º.

6. If a clock shows 4'O clock in the noon. Through how many degrees will the hour hand rotate when the clock shows 12'O clock in the night?

**Answer: **240°

**Explanation:**
4 o'clock noon to 12 o'clock = 8 hrs.

Angle traced by hour hand in 12 hrs. = 360°

so, Angle traced hour hand in 8 hours = (360°/12 * 8) = (120 * 2) = 240°

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

**Answer: **32 8/11 min.

**Explanation:**
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.

8. At what time between 8 and 9'o clock will the hands of a clock be in the same straight line. but not together?

**Answer: **10 1/11

**Explanation:**
When the hands of the clock are in the same line, but in opposite direction, they are 30 minutes spaces apart.

At 8'o clock they are 20 min. spaces apart

minute hand will have to gain only 10 min.spaces

10 min.spaces are gained in [(60/55) * 10] = 120/11 = 10 1/11 past 8.

9. The reflex angle between the hands of a clock at 10.25 is:

**Answer: **197 1/2º

**Explanation:**
Angle traced by hour hand in 12 hrs. = 360°

Angle traced by hour hand in 125 hrs = (360/12 * 125/12)º = 312 1/2º

Angle traced by minute hand in 25 min = (360/60 * 25)º = 150º.

Reflex angle = [360º -(312 1/2 - 150)º = (360º - 162 1/2º = 197 1/2º

10. How many times in a day, the hands of a clock are straight?

**Answer: **44

**Explanation:**
In 12 hours, the hands coincide or are in opposite direction 22 times.

In 24 hours, the hands coincide or are in opposite direction 44 times a day