SOLUTION: Peter and Paul are two friends. The sum of their ages is 35 years. Peter is twice as old as Paul was when Peter was as old as Paul is now. What is the present age of Peter

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Question 338146: Peter and Paul are two friends. The sum of their ages is 35 years. Peter is twice as old as Paul was when Peter was as old as Paul is now. What is the present age of Peter
Answer by J2R2R(94) About Me  (Show Source):
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Supposing Peter’s age is e and Paul’s age is a

We have a + e = 35………………….. (1)

Now when Peter was Paul’s age which means (e - a) years ago

Peter would have been e - (e - a) = a which is Paul’s age now

Paul would have been a - (e - a) = 2a - e

We have been given that Peter’s age is twice what Pauls was,

so e = 2(2a - e) = 4a - 2e which gives 3e = 4a………………….. (2)

For ease of use if a + e = 35; then 3a + 3e = 105 = 3a + 4a from (2) above

Thus 7a = 105

a = 15; e = 20

So Peter is 20 years and Paul is 15 years. The sum is 35 years and when Peter was 15 years Paul would have been 10 years which doubled gives Peter’s age of 20 years now.