A hard question on age problems for P3, with a step-by-step solution, diagrams and the answer. Age problems are common in the Hua Xia Cup's P1 to P4 first and qualifying rounds, and rarer in the P5 and P6 papers.
The question
The older sister says to the younger sister:
"When I was as old as you are now, you were only 1."
The younger sister replies:
"When I'm as old as you are now, you'll be 13."
How old is the younger sister now?
Show the hints (3)
💡Hint 1: Draw a time line with four ages on it: the younger sister at 1, the younger sister now, the older sister now, the older sister at 13.
💡Hint 2: Each step along that line is exactly the age gap between them.
💡Hint 3: From 1 to 13 there are 3 equal steps of 4 years.
Worked solution
Have a go first, then read the solution step by step.
1.Call the age gap "1 step". The older sister was the younger sister's present age 1 step ago, when the younger sister was 1; so the younger sister is now 1 + 1 step.
2.The older sister is 1 step older: the older sister is now the younger sister's age + 1 step = 1 + 2 steps.
3.The younger sister reaches that age 1 step from now, and by then the older sister is 1 step older still: 1 + 3 steps = 13.
4.3 steps = 13 − 1 = 12, so 1 step = 4.
5.The younger sister is 1 + 4 = 5.
6.Check: 9 and 5, 4 apart. 4 years ago: 5 and 1 ✓. In 4 years: 9 and 13 ✓
⚠️Common mistake: taking 13 − 1 = 12 as the gap. There are 3 gaps between 1 and 13.
Play more like this in Numsprite (unlimited questions, instant marking) →A free maths game: every level free from Easy to Expert (★ to ★★★★), unlimited questions, no download