A car weighs 4000 pounds. It was weighed on a defective scale to be 4500 pounds. A truck is weighed on the same scale and found to be 9000 pounds. How much does the truck actually?

Answer 1

Assuming the same rate of error - 8000 pounds !

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Without knowing the actual defect of the scales a definite answer cannot be given.

• If the scales have a defective zero, then the truck weighs 9000 + (4000 - 4500) = 8500 pounds;
• If the scales have a constant defective reading error, then the truck weighs 9000 × (4000 ÷ 4500) = 8000 pounds;
• If the scales have a a defective reading based on reading_weight = e^((ln(4501)/4000)×true_weight) - 1 (ie of the form w = e^(k×wt) - 1), then the truck weighs ln(9001)/(ln(4501)/4000) ≈ 4330 pounds.

For other kinds of faulty reading, a difference real weight of the truck will be found.

Answer 2

The scale can be defective in two main ways.

• The first is a zero error. In this case the scale registers 500 pounds when there is no weight and so the truck which appeared to be 9000 pounds would actually have been 8500 pounds.
  
• The second kind of error is calibration error, where the scale increases the true weight by 12.5%. In that case, the true weight of the truck is 8000 pounds.

Of course, the fault could be any combination of these two (and other) defects and so there is no way to give a definitive answer.