Book Title: Ganitasara Sangraha of Mahavira
Author(s): Rangacharya
Publisher: Rangacharya

Previous | Next

Page 349
________________ CHAPTER VI-XIXED PROBLEMS. 147 optionally chosen varna (of the originally given gold; and then all these products are to be added). From this sum, the sum of the (various) fractional (exchanged) parts (of the original gold) is to be subtracted. (If now) the observed excess (in the weight of gold due to the exchange) is divided by this resulting remainder, what comes out here happens to be the original wealth of gold. An example in illustration thereof. 207-208. A certain small ball of gold of 16 varnas bolonging to a merchant is taken; and 4, and parts thereof are in order exchanged for (different kinds of) gold characterised (respectively) by 12, 10 and 9 varnas. (The weights of these exchanged varieties of gold are) added to what remains (unexchanged) of tho original gold. Then 1,000 is observed to be in excess on removing from the account the weight of the original gold. What thon is (the weight of this) original gold? The rule for arriving at the desired earna with the help of the (mutual) gift of a desired fractional part of the gold (owned by the other), and also for arriving at the (weights of) gold (respectively) corresponding to those optionally gifted parts:-- 209 to 212. One divided by the numerical measure of each of two specifically gifted) parts is to he noted down in reverse order; aud (if each of the quotients so obtained is) multiplied by an 209-212. The rule will be clear from the following working of the problem in 213-815: Dividing 1 by and, we get respectively 2,; altering their position and multiplying them by any optionally chosen number, say 1, we get 2, 2. These two numbers represent the quantities of gold owned respectively by the two merchants. Choosing 9 as the varna of the gold owned by the first merchant, we can easily arrive, from the exchange proposed by him, at 13 as the vary of the gold owned by the second merchant. These varnas, 9 and 13, give, in the exchange proposed by the second merchant, the average varna of, while the average varpa as given in the sum has to be 12 or . If 8 is chosen instead of Therefore the varnas 9 and 13 have to be altered. 9, 13 has to he increased to 18 in the first exchange. Using these two varnas, 8 and 16, in the second exchange, we obtain as the average varna, instead of 14.

Loading...

Page Navigation
1 ... 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531