Question : Here are some problems based on finding the defective machine from given machines. All the machines are identical and produce indentical coins of 10 grams each.
You are given 10 machines. One machine is defective and it produces coins which are heavier or lighter than the other coins by 1 gram. You are given a balance on which the weight can be measured directly. You have to find the defective machine using the balance only once. You should also tell whether the defective coins are lighter or heavier.
Answer : Take 1 coin from the first machine, 2 from the second, 3 from the third and so on. So there will be 55 coins. Weigh them. If all the coins were normal then the weight would have been 550 grams but since some coins are defective the weight may be more or less. We get the following cases.
Case-1: The weight is greater than 550 gram.
This means that one machine produces heavy coins. Calculate the amount by which the weight exceeds 550 gram. If it exceeds by x grams then xth machine is defective.
Case-2: The weight is less than 550 gram.
This means that one machine produces light coins. Calculate the amount by which the weight is less than 550 gram. If it is less by x grams then xth machine is defective.