पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/३६१

CHAPTER VI-MIXED PROBLEMS. 163 confidential language to both the owners of the cocks. He said to one: "If your bird wins, then you give the stake-money to me If, however, you prove unvictorious, I shall give you two-thirds of that stake-money then." He went to (the owner of) the other (cock) and promised to give three-fourths (of his stake-inoney on similar conditions). From both of them the gain to him could be only 12 (gold-pieces in each case). You tell me, O ornament on the forehead of mathematicians, the (values of the) stake-money which (each of) the cock-owners had on hand. The rule for separating the (unknown) dividend number, the quotient, and the divisor from their combined sum - 273 Any (suitable optionally chosen) number (which has to be) subtracted from the (given) combined sum happens to be the divisor (in question). On dividing, by this (divisor) as increased by one, the remainder (left after subtracting the optionally chosen number from the given combined sum), the (required) quotient is arrived at The very same remainder (above mentioned), as dimi- nished by (this) quotient becomes the (required dividend) number. An example in illustration thereof. 274 A certain unknown quantity is divided by a certain (other) unknown quantity. The quotient here as combined with the divisor and the dividend number is 53. What is that divisor, and what (that) quotient? The rule for arriving at that number, which becomes a square either on adding a known number (to the original number), or on subtracting (another) given number (from that same original number) - 275 The sum of the quantity to be added and the quantity to be subtracted is multiplied by one as associated with whatever may happen to be the excess above the even number (nearest to 275 Algebraically, let a be the quantity to be found out, and a, b, the respectivo quantities to be added to or subtracted from it, then, the forumla to represent the rule will be a~6±1 2. { (a + b) + (1+1)÷2} 2 — 1 +1+ ?