A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is:

Angle traced by hour hand in	21	hrs =	❨	360	x	21	❩	°	=	157	1	°
	4			12		4					2

Angle traced by min. hand in 15 min. =	❨	360	x 15	❩	°	= 90°.
		60

∴ Required angle =	❨	157	1	❩	°	- 90° = 67	1	°
			2				2

Angle traced by hour hand in	13	hrs =	❨	360	x	13	❩	°	= 130°.
	3			12		3

Angle traced by min. hand in 20 min. =	❨	360	x 20	❩	°	= 120°.
		60

∴ Required angle = (130 - 120)° = 10°.

Mother's age when Ayesha's brother was born = 36 years.

Father's age when Ayesha's brother was born = (38 + 4) years = 42 years.

∴ Required difference = (42 - 36) years = 6 years.

Let Ronit's present age be x years. Then, father's present age =(x + 3x) years = 4x years.

∴	(4x + 8) =	5	(x + 8)
		2

⟹ 8x + 16 = 5x + 40

⟹ 3x = 24

⟹ x = 8.

Hence, required ratio =	(4x + 16)	=	48	= 2.
	(x + 16)		24

Let the present ages of son and father be x and (60 -x) years respectively.

Then, (60 - x) - 6 = 5(x - 6)

⟹ 54 - x = 5x - 30

⟹ 6x = 84

⟹ x = 14.

∴ Son's age after 6 years = (x+ 6) = 20 years..

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.

At 4 o'clock, the hands of the watch are 20 min. spaces apart.

To be in opposite directions, they must be 30 min. spaces apart.

∴ Minute hand will have to gain 50 min. spaces.

55 min. spaces are gained in 60 min.

50 min. spaces are gained in	❨	60	x 50	❩min. or 54	6	min.
		55			11

∴ Required time = 54	6	min. past 4.
	11

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	❨	60	x 5	❩min	= 5	5	min.
		55				11

∴ Required time = 5	5	min. past 7.
	11

In 12 hours, they are at right angles 22 times.

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

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	x 15	❩min	=	16	4	min.
		55					11

∴ The hands are coincident at 16	4	min. past 3.
	11