# पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/३१७

एतत् पृष्ठम् परिष्कृतम् अस्ति
121
CHAPTER VI--MIXED PROBLEMS.

above division chain. Thus the creeper-like chain of figures required for the solution of this latter combined problem is obtained. This chain is to be dealt with as before from below upwards, and the resulting number is to be divided as before by the first divisor in this last division chain. The remainder obtained in this operation is then) to be multiplied by the divisor (related to the larger group-value, and to the resulting product, this) larger group-value is to be added. (Thus the value of the required multiplier of the given group-number is obtained; and this will satisfy both the specified distributions taken together into consideration).

Examples in illustration thereof.

116${\displaystyle {\tfrac {1}{2}}}$. Into the bright and refreshing outskirts of a forest, which were full of numerous trees with their branches bent down with the weight of flowers and fruits, trees such as jambū trees, lime trees, plantains, areca palms, jack trees, date-palms, hintāla trees, palmyras, punnāga trees and mango trees--(into the outskirts, the various quarters whereof were filled with the many sounds of crowds of parrots and cuckoos found near springs containing lotuses with bees roaming about them (into such forest outskirts) a number of weary travellers entered with joy.

117${\displaystyle {\tfrac {1}{2}}}$. (There were) 63 (numerically equal) heaps of plantain fruits put together and combined with (more) of those same fruits and these were (equally) distributed among 23 travellers so as to leave no remainder. You tell (me now) the (numerical) measure of a heap (of plantains.)

118${\displaystyle {\tfrac {1}{2}}}$. Again, in relation to 12 (numerically equal) heaps of pomegranates, which. after having been put together and

By applying the principle of vallikā-kuṭṭīkāra in the last equation, the value of c is obtained, and thence the value of v can be easily arrived at.

It is seen from this that, when, in order to find out v, we deal with t1 and s3 in accordance with the kuṭṭīkāra method, the chēda or the divisor to be taken in relation to ${\displaystyle t_{1}{\text{ is }}{\tfrac {A_{1}A_{2}}{p}}}$ , or the least common multiple of the divisor in the first two equations