Misrak was looking at the birthdays in her family. After a bit of maths, she realised that her father’s age and her grandfather’s age had the same digits, but swapped.
When she added their ages together, she got 121. Her grandfather was aged between 20 and 40 when her father was born.
• Half of 121 is 60.5, so Misrak’s grandfather is older than 60 and her father is younger than 61.
• To start off, you could try to get the ones digit to work and move on from there.
Let’s start by looking at the ones digit of the ages. We know that the sum of the ages has a ones digit of 1. The ages can’t end with 1 and 0, because swapping digits won’t work. That means the ones digits must add to 11.
We can list all the possible pairs of last digits that add to 11: 5 and 6, 4 and 7, 3 and 8, 2 and 9.
If we know the last digits of both ages, we can work out what the ages are. For example, if the last digits are 5 and 6, the ages are 56 and 65. These add to 121, but this isn’t a good solution because Misrak’s grandfather would only be 9 when her father was born.
If the last digits are 4 and 7, we get 47 and 74 as ages. That adds to 121, indicating Misrak’s grandfather was 28 when her dad was born, so this is a solution that works.
For the remaining pairs, the age gap between father and grandfather more than 40 years: 83 – 38 = 45, and 92 – 29 = 63. We know that’s not the answer because Misrak’s grandfather was aged between 20 and 40 when her father was born.
So Misrak’s father is 47 and her grandfather is 74.
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