Mor haggis: we shall onair thee
Wi’ a cask neart Speyside malt,
A botel o’ whisky o’ twenty year,
Cost’d three score pound of salt.

The botel’s twenty dram do w(h)et
Both appetite and floor,
An’ neither neep nor tattie mop
Th’ ten dram o’ alcol pure:
F’r a litre, th’ Queen duties
Twenty eight an’ sev’nty four
And VAT atop, of twenty
F’r ev’ry hundred ov’r a’.

So wad, fair famished neach, to pay
The sellers, f’r that dram?
And how much thence to th’ Exchequer?
‘Tis worth it, still, for a’ that.

Jim Naughtie read this poem on air, on Friday 25th January, though his version had one or two changes: mostly improvements (“fair famished folk”) but one which took some of the meaning out of the puzzle (“cask of”, instead of “cask neart”).

mor

Great

neart

strength

neep

turnip

tattie

potato

neach

person

Everything else is as it sounds (onair, botel, alcol).

Oh, and the dram is metric. That should not need saying.

Puzzle #402 at the Today programme website.

Puzzle

Today marks the 260th birthday of the Scottish poet Robert Burns. Not just a writer of lyrical, nature-inspired verse, he also worked as an excise officer in Dumfries. This job calculating alcohol duties has inspired today’s puzzle, set by PhD student David Baynard, from the University of Cambridge’s Department of Chemical Engineering and Biotechnology.

Mor haggis: we shall onair thee
Wi’ a cask neart Speyside malt,
A botel o’ whisky o’ twenty year,
Cost’d three score pound of salt.

The botel’s twenty dram do w(h)et
Both appetite and floor,
An’ neither neep nor tattie mop
Th’ ten dram o’ alcol pure:
F’r a litre, th’ Queen duties
Twenty eight an’ sev’nty four
And VAT atop, of twenty
F’r ev’ry hundred ov’r a’.

So wad, fair famished neach, to pay
The sellers, f’r that dram?
And how much thence to th’ Exchequer?
‘Tis worth it, still, for a’ that.

Translation

A 20 year old cask strength (50% ABV) 50 cl bottle of scotch costs £60. Duty on spirits is £28.74 per litre of pure alcohol; VAT is 20%. How much do the merchants and government get from this purchase?

Solution

The whisky costs £60 (three score).

VAT is 20%, or ⅕ of the pre-VAT price, so the total price is 1⅕ (6/5) of the pre-VAT price. ⅚ of this total price is therefore the pre-VAT price, and ⅙ of the total price is VAT. So £10 is VAT. A common error is to say that 20% of the total price is VAT. Also, the pre-VAT price includes the duty.

The bottle contains 20 drams (measures), i.e. 20 × 25 ml = 500 ml. Of that it contains 10 drams of pure alcohol, 250 ml. Incidentally, this corresponds to 50% ABV (alcohol by volume), a ratio of the volume of pure ethanol that would be contained within a drink to the total volume of that drink. Cask strength whiskies are typically in the 50s or 60s %ABV (after 20 years in the barrel one might expect a bottle of scotch to be in the lower end of that range).

For spirits, alcohol duties are charged on the pure alcohol volume, measured as ABV. In this case that means the duty (£28.74 per litre) is charged on the 250 ml (0.25 L), i.e. £28.74 × 0.25 = £7.185.

Rounding on tax is somewhat complicated. The UK government provides guidance on duty calculations for wine, indicating that calculations should be performed to 4 decimal places, volumes should be rounded down to the nearest litre, and then the resulting duty rounded down to the nearest penny. Over an entire business, this rounding error is negligible, but for the purposes of this puzzle, rounding the solution either down to £7.18 or up to £7.19 is acceptable.

Therefore the total payed to the exchequer is £7.18 duty + £10.00 VAT = £17.18. The seller receives the remaining £42.82 (shared with the manufacturer, distributors, etc).