Page:Indian mathematics, Kaye (1915).djvu/68

 remained on the string. Say, of how many pearls the necklace was composed? Answer—30. 5. A powerful, unvanquished, excellent black snake which is 32 hastas in length enters into a hole $$\scriptstyle{7\frac{1}{2}}$$ añgulas in $$\scriptstyle{\frac{5}{14}}$$ of a day, and in the course of a quarter of a day its tail grows by $$\scriptstyle{2\frac{3}{4}}$$ añgulas. O ornament of arithmeticians, tell me by what time this same enters fully into the hole? Answer—$\scriptstyle{76\frac{4}{5}}$|undefined days. (24 añgulas=l hasta.) 6. A certain person travels at the rate of 9 yojanas a day and 100 yojanas have already been traversed. Now a messenger sent after goes at the rate of 13 yojanas a day. In how many days will he overtake the first person? Answer—25. 7. A white-ant advances 8 yavas less one-fifth in a day and returns the twentieth part of an añgula in 3 days. In what space of time will one, whose progress is governed by these rates of advancing and receding proceed 100 yojanas? Answer—98042553 days. (8 yavas=1 añgula, 768000 añgulas=1 yojana). 8. Twenty men have to carry a palanquin two yojanas and 720 dīnāras for their wages. Two men stop after going two krośas, after two more krośas three others give up, and after going half the remaining distance five men leave. What wages do they earn? Answers—18, 57, 155, 490. (4 krośas=1 yojana). 9. It is well known that the horses belonging to the sun's chariot are seven. Four horses drag it along being L=the Līlāvatī, V=Vīja Gaņita, both by Bhāskara, M=Mahāvīra, S=SrīdharaŚrīdhara [sic], C=Chaturveda.