The age of amit is 3 times of ramit and age of ramit is 2 times of sumit and sumit is 10 years younger to amit. find the present age of ramit?

Mathematics
1

the age of amit is 3 times of ramit and age of ramit is 2 times of sumit and sumit is 10 years younger to amit. find the present age of ramit?

2

The age of Amit is 3 times of Ramit and the age of Ramit is 2 times of Sumit and Sumit is 10 years younger to Amit. Find the present age of Ramit?

Answer: Let’s break down the given information and set up equations to solve for the present age of Ramit.

  1. Define Variables:

    • Let ( A ) be the age of Amit.
    • Let ( R ) be the age of Ramit.
    • Let ( S ) be the age of Sumit.

  2. Translate the information into equations:

    • The age of Amit is 3 times the age of Ramit:
      A = 3R
    • The age of Ramit is 2 times the age of Sumit:
      R = 2S
    • Sumit is 10 years younger than Amit:
      S = A - 10

  3. Substitute the equations:

    • From ( R = 2S ), we can express ( S ) in terms of ( R ):
      S = \frac{R}{2}
    • Substitute S = \frac{R}{2} into S = A - 10 :
      \frac{R}{2} = A - 10
    • Now, substitute ( A = 3R ) into the equation:
      \frac{R}{2} = 3R - 10

  4. Solve for ( R ):

    • Multiply both sides by 2 to clear the fraction:
      R = 6R - 20
    • Rearrange the equation to isolate ( R ):
      R - 6R = -20
      -5R = -20
      R = 4

Therefore, the present age of Ramit is \boxed{4} years.