Question

Ravish tells her daughter Aarushi "three years from now I shall be two times as old as he was 4 years ago".If present ages of Aarushi and Ravish are X and Y years , represent info algebraically​

Answer 1

Let the age of Aarushi be ‘x’ years and age of Ravish be ‘y’ years

7 years ago age of Aarushi = (x – 7) years

7 years ago age of Ravish = (y – 7) years

Given (y – 7) = 7(x – 7)

⇒ y – 7 = 7x – 49

⇒ 7x – y – 42 = 0 → (1)

3 years later age of Aarushi = (x +3) years

3 years ago age of Ravish = (y + 3) years

Given (y + 3) = 3(x + 3)

⇒ y + 3 = 3x + 9

⇒ 3x – y + 6 = 0 → (2)

Subtract (2) from (1), we get

7x – y – 42 = 0

3x – y + 6 = 0

-------------------

4x – 36 = 0

∴ x = 9

Put x = 9 in (2), we get

3(9) – y + 6 = 0

⇒ 27 – y + 6 = 0

∴ y = 33

Hence present age of Aarushi is 9 years and present age of Ravish is 33 years.