Question

Vani, her father and her grandfather have an age of 53. One- half of her grandfather's age plus one-third of her father's age plus one fourth of vani's age is 65. Four years ago if vani's grandfather was four times as old as vani then how old are they all now?

Answer 1

Answer:

Step-by-step explanation:let vani age be x, father age be y,grand father age be z.

Then,

(x+y+z)/3 = 53

x+y+z = 53×3

x+y+z = 159...............eqn 1

(1/2)z+ (1/3)y + (1/4)x = 65

(3x + 4y + 6z)/12 = 65

3x+4y+6z = 780.......eqn2

4 years ago vani age and grand father age be x-4 & y-4 then eqn be

z-4 =4(x-4)

z-4 = 4x - 16

4x - z = 16 - 4

4x - z = 12.... eqn 3

Solve 1 and 2 by eliminating ' y ' we get

x-2z = -144 ........... eqn 4

Solve 3 & 4 we get

-7x = -168

x = 24

Sub x value in eqn 2 we get z= 84

Substitute x and z value in eqn 1 we get

y = 51.

Therefore vani age is 24 yrs

Father's age is 51 yrs

Grand father's age 84 yrs