The Age Old Problem
Algebra
Level
4
The combined ages of Amit & Mohan are 56 years. Amit is twice as old as Mohan was when Amit was half as old as Mohan will be when Mohan is three times as old as Amit was when Amit was three times as old as Mohan.
What is the age of Mohan???
The answer is 21.
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1 solution
Let's start from end: 'amit was 3 times as old as mohan'.
At this stage, let mohan=x years & amit=3x years.
Difference in age=2x years (which always remains constant)
...'when mohan is 3 times as old as amit was...'
Mohan is 3(3x)=9x
....'amit was 1/2 as old as mohan will be...'
Amit was 9x/2=4.5x and mohan therefore was 4.5x-2x=2.5x
...'amit is twice as old as mohan was...'
Amit is 2(2.5x)=5x and mohan is 5x-2x=3x
5x+3x=56
x=7
Mohan is 3x=21 years