When I was six, my sister was half my age

Question

"When I was 6 years old, my sister was half my age. Now I am 70." How old is the sister? The instant answer of 35 is wrong; say exactly what mistaken assumption produces it, and what quantity in any age puzzle never changes.

Accepted Answer

She is 67. The gap. When the speaker was 6, the sister was half of 6, which is 3. So she is 3 years younger, and that difference never changes. Now the speaker is 70, so she is 70 minus 3 = 67. Why 35 is tempting. "Half my age" sounds like a permanent ratio, and 70 divided by 2 is 35. But ratios of ages change every year (a 3-year-old is half a 6-year-old, a quarter of a 12-year-old, a tenth of a 30-year-old); only the difference stays fixed. Every age puzzle is really about that fixed difference. A relative. "A father is four times his son's age now; in 20 years he will be twice as old. How …

When I was six, my sister was half my age

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