PK 2018 Q2
2. The distance from the top of the can on the floor to the top of the bottle on the table is 150 cm. The distance from the top of the bottle on the floor to the top of the can on the table is 110 cm. What is the height of the table?
- A 110 cm
- B 120 cm
- C 130 cm
- D 140 cm
- E 150 cm
Pink Kangaroo 2018, Question 2. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 130 cm
Let \(t\) be the height of the table, \(b\) the height of the bottle and \(c\) the height of the can (all measured in cm). The first diagram shows \(t + b = c + 150\); the second diagram shows \(t + c = b + 110\). Adding these equations gives \(2t + b + c = 260 + b + c\) so \(2t = 260\). So the table has height 130 cm.
Solution © UK Mathematics Trust, from the PK 2018 solutions.