There are four types of weights, namely 1 kg, 2 kg, 5 kg and 10 kg. What is the maximum number of different ways one can measure…

Question

There are four types of weights, namely 1 kg, 2 kg, 5 kg and 10 kg. What is the maximum number of different ways one can measure 20 kg, if at least eight but not more than eleven weights of 1 kg are to be used while measuring?

1. A. 7
2. B. 8 (Correct answer)
3. C. 9
4. D. 10

Correct Answer

Option B — 8

Detailed Solution & Explanation

The correct answer is Option B (8 ways).

Key Points

• Weights available: 1, 2, 5, 10 kg; total needed = 20 kg using 8 to 11 one-kg weights.
• For each allowed count of 1-kg weights, the remaining kilograms must be formed from 2s, 5s and 10s, and counting the valid partitions across 8, 9, 10 and 11 one-kg weights gives 8 distinct ways.

Additional Information

• Restricting the number of 1-kg weights is what bounds the count to 8 → Option B.