Henry Ernest Dudeney/Modern Puzzles/186 - The False Scales/Solution 2

by : $186$

 * The False Scales

Solution
Suppose that the false balance has unequal arms.

That is, the arms are of different length.

Then the true weight of the pudding is $143$ ounces.

Proof
Let $W$ ounces be the true weight of the pudding.

We are given that:
 * in one pan the apparent weight was $\dfrac {9 W} {11} + 4$


 * in the other pan the apparent weight was $\dfrac {9 W} {11} + 52$.

Hence we have:

Hence the result.