《孫子算經卷下》 "Sun Tzŭ's Computational Classic: Volume III"
§14. Division determining a rate (4)

This section gives a word problem where division is used to determine a rate.

The relevant unit conversion for weight is

1 \unit{catty~(斤)} = 16 \unit{taels~(兩)}.

See Vol. I §2 (Units of weight).

Translation

Chinese source text: Version A, Version B, Version C, Version D.
Unless noted otherwise, I follow the text from Version D, 《知不足齋叢書》本.

Source text Target text Notes
今有貸與人絲五十七斤、限歲出息一十六斤。問斤息幾何。 Suppose there be [a] loan giving [a] person silk fifty-seven catties, [with] limit of [a] year [to] supply [the] interest of sixteen catties. [We] ask, how much [be each] catty's interest?
答曰、四兩五十七分兩之二十八。 Answer saith: four taels [and] twenty-eight fifty-sevenths of [a] tael.
術曰、列限息絲一十六斤、以一十六兩乘之、得二百五十六兩。 Method saith: rank [the] limit's interest of silk, [even] sixteen catties; multiplying it by sixteen taels, resulteth in two hundred [and] fifty-six taels.
以貸絲五十七斤除之、不盡、約之、即得。 Dividing it by [the] loaned silk fifty-seven catties, [there be a] remainder; reducing it, [we] are done.
  • Version A is missing 七 in 五十七斤.
  • Version C erroneously has ⑤ U+2464 after 除之.
  • 不盡： [there be a] remainder; lit. exhausteth not
  • In modern notation,
    \frac{ 16 \unit{catties} \times 16 \unit{taels} / {\unit{catty}} }{ 57 \unit{catties} } = \frac{4 \frac{28}{57} \unit{taels}}{\unit{catty}}.
    The fraction 28/57 is already irreducible, so the instruction 約之 "reduce it" is actually superfluous.

Cite this page

Conway (2023). "Sun Tzŭ's Computational Classic: Volume III §14". <https://yawnoc.github.io/sun-tzu/iii/14> Accessed yyyy-mm-dd.