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?
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.
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Define Variables:
- Let ( A ) be the age of Amit.
- Let ( R ) be the age of Ramit.
- Let ( S ) be the age of Sumit.
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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
- The age of Amit is 3 times the age of Ramit:
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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
- From ( R = 2S ), we can express ( S ) in terms of ( R ):
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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
- Multiply both sides by 2 to clear the fraction:
Therefore, the present age of Ramit is \boxed{4} years.