Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?

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..

Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.

∴ (2x + 2) + 2x + x = 27

⟹ 5x = 25

⟹ x = 5.

Hence, B's age = 2x = 10 years.

Let their present ages be 4x, 7x and 9x years respectively.

Then, (4x - 8) + (7x - 8) + (9x - 8) = 56

⟹ 20x = 80

⟹ x = 4.

∴ Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively.

Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.

Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50

⟹ 5x = 20

⟹ x = 4.

∴ Age of the youngest child = x = 4 years.

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°.

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

Time from 7 a.m. to 4.15 p.m. = 9 hrs 15 min. =	37	hrs.
	4

3 min. 5 sec. of this clock = 3 min. of the correct clock.

⟹	37	hrs of this clock =	1	hrs of the correct clock.
	720		20

⟹	37	hrs of this clock =	❨	1	x	720	x	37	❩	hrs of the correct clock.
	4			20		37		4

      = 9 hrs of the correct clock.

∴ The correct time is 9 hrs after 7 a.m. i.e., 4 p.m.

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