The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).

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.

Let Rahul's age be x years.

Then, Sachin's age = (x - 7) years.

∴	x - 7	=	7
	x		9

⟹ 9x - 63 = 7x

⟹ 2x = 63

⟹ x = 31.5

Hence, Sachin's age =(x - 7) = 24.5 years.

Let the present ages of Arun and Deepak be 4x years and 3x years respectively. Then,

4x + 6 = 26    ⟺    4x = 20

x = 5.

∴ Deepak's age = 3x = 15 years.

Let the son's present age be x years. Then, (38 - x) = x

⟹ 2x = 38.

⟹ x = 19.

∴ Son's age 5 years back (19 - 5) = 14 years.

Let the son's present age be x years. Then, man's present age = (x + 24) years.

∴ (x + 24) + 2 = 2(x + 2)

⟹ x + 26 = 2x + 4

⟹ x = 22.

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 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 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

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.

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°.