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Today Puzzle #672

Puzzle No. 672– Monday 10 February

Alicia, Bea and Celia all have the same birthday as their mother. However, they all get annoyed at their shared birthday party when people ask their ages, so they invented a riddle: One of us is three times the age of another. One is double the age of the youngest. All our ages today add up to our mum’s age which is 48. How old are the girls?

Today’s #PuzzleForToday has been set by Dr Nicos Georgiou, a senior mathematics lecturer from the University of Sussex.

Click here for the answer

Let x and 2x denote the ages of the two girls who one has double the age of the other. We know x is the youngest. Then the third girl has age either 3x or 6x since she must be different than the two considered. In the first case, their age sum is 6x, while in the second case, their age sum is 9x. So, the smallest age x, must satisfy 9x= 48 (i.e. x = 48/9) or 6x = 48 (i.e. x = 8). Since its their birthday, their age must be a whole number, so it has to be that x = 8, 2x = 16, and 3x = 24.

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