Q.26. Simultaneous equations

Question 26.
John tells Peter:
I have two times the age you had when I had your actual age.
When you reach the age i have now the addition of our ages will be 63 years.
Which are the ages of John and Peter ?


Answer 26.
Let the age of John = x years
and the age of Peter = y years
 
From the given conditions,
x = 2 [ y - (x - y) ] and x + x + (x - y) = 63
=> 3x = 4y and 3x = 63 + y
Solving, y = 21 and x = 28

Answer: John is 28 years and Peter is 21 years worked out as under.

Verification:
John had Peter's age x -y = 7 years back when Peter was 14. John now is 2 times of 14 satisfies condition 1.
Peter will reach John's age after x - y = 7 years when the age of John will be 35 and that of Peter will be 28 and the sum of their ages will be 63. This satisfies condition 2.

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