type 2 position of hands of the clock Detailed Explanation And More Example

Answer: (c)

In 12 hours, they are at right angles 22 times

Therefore, In 24 hours, they are at right angles 44 times.

Answer: (c)

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

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

Answer: (b)

Clearly, the minute hand traverses 65 minutes in 1 hour.

Therefore, Required angle = (360/60 × 65). = 390.

Answer: (c)

Both the hands are 15 min spaces apart at 9 O' clock. To be together between 9 and 10 min O' clock hand has to gain 45 min.

Now, minute hand gains 55 min in 60 min. Therefore, it will gain 45 min in $60/55 × 45 = 49 1/11 min$

Therefore, the hands will be together at 49 $1/11$ min past 9.

Answer: (a)

Fig (i) shows the positions of the hands of the clock at 8 O' clock and it is clear that they are 20 min apart. To be in the straight line, they have to be 30 min apart.

So, the minute hand will have to gain 10 min space in order to be 30 min apart from hour hand. Since 55 min are gained in 60 min,

Therefore, 10 min will be gained in $60/55 × 10 = 12/11 × 10 min $

Therefore, the hands will be in straight line but not together at $10 10/11 $min past 8.

Answer: (d)

At 3 O' clock both the hands of the clock are 15 min apart. Hence, in order to be together, minute hand will have to gain 15 min spaces in order to coincide with the hour hand. Now, 55 min are gained by minute hand in 60 min.

Therefore, 15 min will be gained in $(60/55 × 15) min = (12/11 × 15) min $= $180/11 or 16 4/11 min$

Therefore, the hands will coincide at 16$ 4/11$ min past 3.