Clocks Questions

Angle traced by the hour hand in 6 hours=(360/12)*6

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 min. spaces.
55 min. spaces are gained in 60 min.

5 min spaces are gained in 6055*5 min  = 5511min 

so, Required time = 5511 min  past 7

To be together between 9 and 10 o'clock, the minute hand has to gain 45 min. spaces.
55 min. spaces gained in 60 min.

45 min. spaces are gained in 6055×45 min  or 49111min

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 6055×40 min  

Angle traced by hour hand in214 21 hrs = 36012×2140 =157102 

Angle traced by min. hand in 15 min = 36012×150 = 900 

 Required Angle = 157120-900 = 67102

Angle traced by hour hand in 17/2 hrs = 36012×172o = 255 

Angle traced by min hand in 30 min = 36060×30o = 180 

Therefore,  Required angle = (255 - 180) = 75o

this type of problems the formulae is
(5*x + or -15)*(12/11)
Here x is replaced by the first interval of given time
here i.e 4
Case 1 : (5*x + 15)*(12/11)
(5*4 +15)*(12/11)
(20+15)*(12/11)
35*12/11=420/11=38 2/11 min.
Therefore they are right angles at 38 2/11 min .past4
Case 2 : (5*x-15)*(12/11)
(5*4-15)*(12/11)
(20-15)*(12/11)
5*12/11=60/11 min=5 5/11min
Therefore they are right angles at 5 5/11 min.past4.

At 3 o'clock, the minute hand is 15 min. spaces apart from the hour hand.
To be coincident, it must gain 15 min. spaces.55 min. are gained in 60 min.
15 min. are gained in
= (60/55 x 15)min
=16+4/11
The hands are coincident at 16 + 4/11 min past 3