Question

the ages of two friends arun and ajith differ by 2years. arun father is twice as old as arun and ajith is twice as old as his brother shiva. tha ages of arun father and shiva differ by 40 years. find the ages of arun and ajith​

Answer 1

Let the age of arun be x years

Let the age age of ajith be y years

Difference of age between ajith and arun = 2 years

x - y = 2

x = 2 + y--- eq(1)

Arun's father age is twice the age of arun = 2(x)

Ajith's age is twice the of age of his brother shiva.

It means ajith's brother shiva age is half of the age of ajith = y/2

Difference of age between arun's father and shiva = 40 years

2x - y/2 = 40 years

2(2 + y) - y/2 = 40 (From eq(1))

4 + 2y - y/2 = 40

{(4 + 2y)2 - y}/2 = 40

(8 + 4y - y)/2 = 40

8 + 4y - y = 40 * 2

3y = 80 - 8

3y = 72

y = 72/3

y = 24

So ajith age = y = 24 years

Substitute y = 24 in eq(1) to know the age of arun

x = 2 + 24 = 26 years

So arun's age = 26 years

Verification:

Verification for first statement :

x - y = 2

26 - 24 = 2

2 = 2

first statement satisfied

Verification for second statement :

2x - y/2 = 40 years

2(26) - 24/2 = 40

52 - 12 = 40

40 = 40

second statement is satisfied.