The original question was too long to copy in. It was: "The sum of the ages of Old and Young is 48. Old is twice as old as young was when old was half as old as young will be when young is three times as old as old was when old was three times as old as young How old is old?" There is a rather strenuous algebraic solution.

The answer is :Old is 30, Young is 18

When Old was 18, Young was 6; when Old was 27 (1/2 of 54), Young was 15, and Old is twice that.

If you change the sum to 32, then the ages become 20 and 12.

When Old was 12, Young was 4; when Old was 18 (1/2 of 36), Young was 10.

In each case, Old is always 5/3 as old as Young and 5/8 of the sum.

* To get a numerical answer, you would need to know the sum of their ages, which was given as 48 in the original form of this question, where Old is 30, Young is 18.

When Old was 18, Young was 6; when Old was 27 (1/2 of 54), Young was 15, and Old is twice that.

If you change the sum to 32, then the ages become 20 and 12.

When Old was 12, Young was 4; when Old was 18 (1/2 of 36), Young was 10.

In each case, Old is 5/3 as old as Young and 5/8 of the sum of their ages.

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Old = 2 * Young when Old was 1/2 [3 * (3 * Young)]

(see the related link for one solution)