# पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/३४८

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152
GAŅITASĀRASAŃGRAHA.

measured in) yōjana, subtract the (continued) product of (the numerical value of) the weight to be carried, (that of the stipulated) wages, the distance already gone over, and the distance still to be gone over. Then, if the fraction ( viz., half) of the weight to be carried over, as multiplied by the (whole of the stipulated) distance, and then as diminished by the square root of this (difference above mentioned), be divided by the distance still to be gone over, the required answer is arrived at.

An example in illustration thereof.

227. Here is a man who is to receive, by carryiug 32 jackfruits over 1 yōjana, 7${\displaystyle {\tfrac {1}{2}}}$ of them as wages. He breaks down at half the distance. What (amount within the stipulated wages) is (then) due to him ?

The rule for arriving at the distances in yōjanas (to be travelled over) by the second or the third weight-carrier (after the first or the second of them breaks down):-

228. From the product of the (whole) weight to be carried as multiplied by the (value of the stipulated) wages, subtract the square of the wages given to the first carrier. This (difference has to be used as the) divisor in relation to the (continued) product of the difference between the (stipulated) wages (and the wages already given away), the (whole) weight to be carried, and the (whole) distance (over which the weight has to be carried. The resulting quotient gives rise to the distance to be travelled over by the second (person).

An example in illustration thereof.

229. A man by carrying 24 jack-fruits over (a distance of) five yōjanas has to obtain 9(of them) as wages therofor. When 6 of these have been given away as wages (to the first carrier), what is the distance the second carrier has to travel over (to obtain tho remainder of the stipulated wages) ?

228. Algebraically ${\displaystyle D-d={\tfrac {(b-x)aD}{ab-x^{2}}}}$, which can be easily found out from the equation in the last note.