Question

5 years earlier ram was three times older than shyam . the age of ram will twice the age of shyam after 10 years. what is the present age of ram and shyam?

Answer 1

Solution:

Let age of Shyam = x years

Let age of ram  be y years.

5 Years ago

Age of Shyam = (x - 5) years

Age of Ram = (y -5) years

As Ram was three times older than Shyam 5 years ago.

→ y -5  = 3 (x -5)

→y -5 = 3 x  - 15  [ Using distributive property]

→ y - 3 x = - 15 + 5

→ y - 3 x = -10

After 10 years

age of ram = (y + 10) years

Age of shyam = (x +10) years

10 years after, age of ram will twice the age of Shyam .

→ y + 10 = 2 × ( x +10)

→ y + 10 = 2 x + 20

→ y - 2 x = 20 -10

→ y - 2 x = 10 -------(1)

→y - 3 x = - 10 ----------(2)

Subtracting  (1) from (2), we get

→ - x = -20

gives , x = 20

Putting the value of x in equation (1)

→y - 2 × 20 = 10

→ y - 40 = 10

→ y = 40 + 10

→ y = 50

Present age of Ram = 50 years

Present age of Shyam = 20 years