Problem 24 · 2018 Math Kangaroo
Stretch
Logic & Word Problems
balance-scalelogic
Each of the four balls weighs either 10, 20, 30 or 40 grams. The two balances are shown. Which ball weighs 30 grams?
Show answer
Answer: C — C
Show hints
Hint 1 of 3
The four weights 10, 20, 30, 40 add up to 100 grams altogether — keep that total handy.
Still stuck? Show hint 2 →
Hint 2 of 3
The second scale is level, so the two balls on one side weigh exactly as much as the single ball C on the other side.
Still stuck? Show hint 3 →
Hint 3 of 3
Try out which single weight can be split into two of the other weights, and check it against the tilted first scale.
Show solution
Approach: use the level scale to say C equals two other balls added, then test which weight that can be
- The second scale balances, so B and D together weigh the same as C alone — that means C is made by adding two of the other weights.
- Among 10, 20, 30 and 40, the only weight that is the sum of two of the others is 30 = 10 + 20, so C must be 30 grams (with B and D being 10 and 20, leaving A as 40).
- Check the first scale: A and B together (40 + 20 = 60) are heavier than C and D (30 + 10 = 40), and that side does tip down, so everything fits — the 30 gram ball is C.
Mark:
· log in to save