Henry Ernest Dudeney/Modern Puzzles/186 - The False Scales/Solution
Modern Puzzles by Henry Ernest Dudeney: $186$
- The False Scales
- A pudding, when placed into one of the pans of a balance, appeared to weigh $4$ ounces more than $\tfrac 9 {11}$ of its true weight,
- What was its true weight?
Solution
Let $W$ ounces be the true weight of the pudding.
Note that we are discussing the weight of a pudding.
Hence the everyday avoirdupois scale is to be used.
First recall that there are $16$ ounces (avoirdupois) to the pound (avoirdupois).
Hence $3$ pounds more than in the first pan means $\tfrac 9 {11} W + 4 + 3 \times 16$, that is, $\tfrac 9 {11} W + 52$.
There are two different solutions to this puzzle, depending on how the false balance is faulty.
Solution 1: Unequal Weight of Pans
Suppose that the false balance has imbalanced pans.
That is, the pans are of different weight.
Then the true weight of the pudding is $154$ ounces.
Solution 2: Unequal Arms
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.
Sources
- 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Solutions: $186$. -- The False Scales
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $97$. The False Scales