Age Problem

This item is taken from IGCSE Mathematics (0580) Paper 31 of May/June 2013.


To deal with this item, let us summarize the details of the problem:
   (a) Syllabus area: Algebra
   (b) Specific topic: Age Problems
Let us first complete the table for (a)(i). The difference between 2013 and 2001 is 12. In other way, if 1 is added to 2001, the result if 2013. Hence, if 2001 is represented by x, then 2013 is represented by x + 12.

For Ken's age on 2001, let us go back to the given in the problem: "Ken is 34 years younger than Arnold". In other words, the difference of their ages is 34. The age of Ken on 2013 can also be calculated by adding 12 to his age on 2001.

For (a)(ii), let us use the expressions for their ages on 2013. Arnold is (x + 12) and Ken is (x - 22) years old. By that time, Arnold is "three times"  as old as Ken. It means that to get the age of Arnold, multiply the age of Ken by three.

Solving for the value of x.

Therefore, the value of x is 39, which is the age of Arnold on 2001.

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