Rami and Grandpa: two age puzzles
✓ With solution
An age three years from now, and a grandpa counted in years while his grandson is counted in months. Can you solve them without pen and paper?
In 3 years, Rami will be twice as old as he was 3 years ago. How old is Rami today?
- A6
- B9
- C12
- D15
Show the answer
Answer: B) 9. Call Rami's age today x. In 3 years he'll be x + 3; 3 years ago he was x − 3. So x + 3 = 2 × (x − 3), which means x + 3 = 2x − 6, so x = 9. Check: 3 years ago he was 6, in 3 years he'll be 12, and 12 is twice 6. A quicker way: the two ages are 6 years apart and one is double the other, so they are 6 and 12, and today Rami is halfway between: 9.
Grandpa's age in years is the same number as his grandson's age in months. Together they are 65 years old. How old is Grandpa?
- A52
- B58
- C60
- D65
Show the answer
Answer: C) 60. A year has 12 months, so if the grandson's age in months equals Grandpa's age in years, Grandpa is 12 times as old. If the grandson is x years old, Grandpa is 12x, and together 13x = 65, so x = 5. The grandson is 5 (that's 60 months) and Grandpa is 60. Check: 5 + 60 = 65.
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