Henry Ernest Dudeney/Puzzles and Curious Problems/22 - The War Horse/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $22$

The War Horse

Farmer Wurzel bought a old war horse for $\pounds 13$ and sold it later for $\pounds 30$.

After having paid for its keep, it turned out he lost half the price he paid and one-quarter the cost of his keep.

How much did Farmer Wurzel lose on the transaction?

Solution

$\pounds 14, 6 \shillings 8 \oldpence$

Proof

Let $L$ be the loss made on the warhorse in pounds.

Let $K$ be the cost of the upkeep of the warhorse in pounds.

Then we have:

\(\text {(1)}: \quad\)

\(\ds L\)

\(=\)

\(\ds 13 - 30 + K\)

Farmer Wurzel bought a old war horse for $\pounds 13$ and sold it later for $\pounds 30$ ... After having paid for its keep ...

\(\text {(2)}: \quad\)

\(\ds L\)

\(=\)

\(\ds \dfrac {13} 2 + \dfrac K 4 + K\)

... he lost half the price he paid and one-quarter the cost of his keep.

\(\ds \leadsto \ \ \)

\(\ds 4 L\)

\(=\)

\(\ds 26 + K\)

simplifying $(2)$

\(\ds K\)

\(=\)

\(\ds L + 17\)

simplifying $(1)$

\(\ds \leadsto \ \ \)

\(\ds 4 L\)

\(=\)

\(\ds 26 + L + 17\)

substituting for $K$

\(\ds \leadsto \ \ \)

\(\ds 3 L\)

\(=\)

\(\ds 43\)

simplifying

\(\ds \leadsto \ \ \)

\(\ds L\)

\(=\)

\(\ds \dfrac {43} 3\)

simplifying

\(\ds \)

\(=\)

\(\ds 14 \tfrac 1 3\)

Converting the result into pounds and shillings reveals the solution.

$\blacksquare$

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $22$. -- The War Horse