Mathematical Reasoning
A balance has two identical pans.
Question 1 · Multiple choice
Question
A balance has two identical pans.
Left pan: masses of 8 kg and 13 kg.
Right pan: masses of 6 kg and 11 kg.
Which one change would make the scales balance?
Options
- A.Add 4 kg to the right pan.
- B.Add 4 kg to the left pan.
- C.Move 3 kg from the left pan to the right (total mass unchanged).
- D.Remove 3 kg from the left pan only.
- E.Add 6 kg to each pan.
Correct answer
A.Add 4 kg to the right pan.
Explanation
Step 1: Find the weight on each pan
Left pan: 8 + 13 = 21 kg
Right pan: 6 + 11 = 17 kg
Left (21 kg) Right (17 kg)
↓ ↑
↘────────────────────↗
scales tilt left (4 kg too heavy)
Step 2: Find the imbalance
Left − Right = 21 − 17 = 4 kg
The left side is 4 kg heavier. To balance, the right side needs to gain 4 kg.
Step 3: Check which action fixes this
Adding 4 kg to the right pan: Right = 17 + 4 = 21 kg = Left ✓
Answer: Add 4 kg to the right pan