Question

Five years ago, Neeta was trice as old as Reeta. Ten years later, Neeta will be

twice as old as Reeta, how old are Neeta and Reeta now?​

Answer 1

Let the present age of Neeta be x

Let the present age of Reeta be y.

Five years ago,

The age of Neeta will be x-5

The age of Reeta will be y-5

Five years ago, Neeta was thrice as old as Reeta.

$x - 5 = 3 \times (y - 5) \\ \\ x - 5 = 3y - 15 \\ \\ x = 3y - 15 + 5 \\ \\ x = 3y - 10$

Let the above equation be 1

After ten years,

The age of Neeta will be x+10

The age of Reeta will be y+10

Ten years later, Neeta will be twice as old as Reeta

$x + 10 = 2 \times (y + 10) \\ \\ x + 10 = 2y + 20 \\ \\ x = 2y + 20 - 10 \\ \\ x = 2y + 10$

Let the above equation be 2.

Substitute equation 1 in 2.

$3y - 10 = 2y + 10 \\ \\ 3y = 2y + 10 + 10 \\ \\ 3y - 2y = 20 \\ \\ y = 20$

The present age of Reeta is 20.

Now substitute y = 20 in any of the equation.

Let us substitute in equation 2.

$x = 2y + 10 \\ \\ x = 2(20) + 10 \\ \\ x = 40 + 10 \\ \\ x = 50$

The present age of Neeta is 50.

ANSWER:

At present, Neeta is 50 years old and Reeta is 20 years old.