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,

but when placed into the other pan it appeared to weigh $3$ pounds more than in the first pan.

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