पाटीगणित (श्रीधराचार्य - प्राचीन संस्कृत टीका एवं प्रो. कृपाशंकर शुक्ल सविस्तार व्याख्या)

• MIXTURES. WAGES PAID FROM COMMODITY 57
  or, (d - d₁) x² - adx + awd₁ = 0 ,
  whence x = [ad/2 ± √((ad/2)² - awd₁ (d - d₁))] / (d - d₁) .
  Taking the negative sign before the radical, we have the rule stated
  above. The positive sign is rejected because it makes x > w.
  Ex. 92. If for carrying 24 jack-fruits over a distance of
  5 krośas (a porter) is to get 9 of those jack-fruits, what will
  he get if he carries them over a distance of 2 krośas (only) ?¹
  Rule for finding the distances over which two porters carry
  a commodity in turn, when the wages paid to the porters
  out of the commodity carried by them are given :

71. The first and the second loads (i.e., the loads carried
    by the first and the second porters), each multiplied by
    the wages for the other, being added together, the resul-
    ting sum is (to be taken as) the divisor (of the following
    results) : the results obtained by multiplying the products
    of the wages received (for each of the loads) and the
    (total) distance (gone over by the porters), each by the other
    load. This gives the distances (gone over by the first and the
    second porters separately).²
    Suppose that the first porter carries a articles over a distance x
    (unknown) and gets b articles out of those a articles as wages, and that
    the second porter carries the remaining a - b articles over the remaining
    distance d - x and gets c articles as wages. Then, we have
    c = b(a - b)(d - x) / ax ,
    whence x / ((a - b)b) = (d - x) / ac = d / (ac + (a - b)b)
    Hence the above rule.
    Ex. 93-94. Twenty-four jack-fruits were carried (over
    a certain distance) by one (person) for 4 out of those (24) jack-
    fruits as wages ; the remaining jack-fruits were carried (over
    the remaining distance) by another person for 5 of them (as
    wages). The load was thus carried by the two (person) over

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¹ Cf. GSS, vi. 227. Also see GK, I, p. 103, lines 17-20.
² See GSS, vi. 228.