Question

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Five years ago, Ajay was thrice as old as Sonu. Ten years later, Ajay will be twice as old as Sonu. How old are Ajay and Sonu?​

Answer 1

Step-by-step explanation:

To find:

• Age of Ajay and Sonu

Solution:

Let the present age of Ajay be x years,

Then, present age of Sonu be y years

Five years ago,

⇛Age of Ajay = x-5 years

⇛Age of Sonu = y-5 years

• Ajay was thrice as old as Sonu

⇛ x - 5 = 3(y-5)

⇛ x - 5 = 3y - 15

⇛x - 3y = -15 + 5

⇛ x - 3y = -10 .... i

Ten years later,

⇛ Age of Ajay = x+10

⇛ Age of Sonu = y+10

• Ajay will be twice as old as Sonu

⇛ x + 10 = 2(y+10)

⇛ x + 10 = 2y + 20

⇛ x - 2y = 20 - 10

⇛ x-2y = 10 .... ii

Now,

⇛ x-2y = 10 ... i

⇛ x-3y = -10 ... ii

Subtracting equation i from equation ii,

We get,

⇛ Y = 20

Plug this value in equation i,

⇛ x - 3×20 = -10

⇛ x = 60-10

⇛ x = 50

Hence, Age of Ajay = 50 years

And, Age of Sonu = 20 years