पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/३१३

CHAPTER VI--MIXED PROBLEMS. 115 The rule for arriving at the value of the prices producing equal sale-proceeds when the price of the remnant is fractional in character: 107 When the remnant-price is fractional in character, the selling and the buying rates are to be derived as before with (the data consisting of) the (invested) capitals and the remnant-price reduced to the same denominator, which is (however) ignored (for the time being); these selling and buying rates are (theu re- spectively) to be multiplied by (this) denommator and the square of (this) denominator (fos arriving at the required selling and buy- ing rates). The value of the cqual sale-proceeds is (then obtained) by means of the rule-of-three. An example in illustration thereof. 108 (In a transaction), are the capital amounts (invested respectively by three persons); the remnant-price 18. By purchasing and selling at the same prices, they became possessed of cqual sale-proceeds (What is the buying price, what the selling price, and what the equal sale-amount ?) Again, another rule for arriving at the value of the equal sale- proceeds, when the remnant-price is fractional - 109. The continued product of the highest numerator, of two, and of (all) the denominators (to be found in the values of the capital amounts invested), when combined with the (last) denomi- nator belonging to the value of the remnant-price, gives rise to the selling rate. This multiplied by the remnaut-price, and then diminished one, and then multiplied (successively) two and all the denominators, becomes the purchasing rate Then the rule-of-three (is to be used for arriving at the common value of the sale-amounts). An example in illustration thereof. 110. Having invested ,, (respectively), and having bought and sold (the same commodity), and with as the remnant- price, three merchants became possessors of equal sale-proceeds