Page:Indian mathematics, Kaye (1915).djvu/72

 26. Of two arithmetical progressions with equal sums and the same number of terms the first terms are 2 and 3, the increments 3 and 2 respectively and the sum 15. Find the number of terms? Answer—3. 27. A merchant pays on certain goods at three different places. At the first he gives $$\scriptstyle{\frac{1}{3}}$$ of the goods, at the second $\scriptstyle{\frac{1}{4}}$,|undefined and at the third $\scriptstyle{\frac{1}{5}}$.|undefined The total duty paid is 24. What was the original amount of the goods? Answer—40. 28. One says: "Give me a hundred and I shall be twice as rich as you, friend!" The other replies: "If you deliver ten to me I shall be six times as rich as you. Tell me what was the amount of their respective capitals? Answer—40 and 170. 29. A gives a certain amount, B gives twice as much as A, C gives 3 times as much as B, D gives 4 times as much as C and the total is 132. Answer—A gives 4, etc.  30. Four jewellers possessing respectively 8 rubies, 10 sapphires, 100 pearls and 5 diamonds, presented each from his own stock one apiece to the rest in token of regard and gratification at meeting; and thus they became owners of stock of precisely the same value. Tell me, friend, what were the prices of their gems respectively? Answer—24, 16, 1, 96 [These are relative values only].  31. The quantity of rubies without flaw, sapphires, and pearls belonging to one person, is five, eight and seven  L=the Līlāvatī, V=Vīja Gaņita, both by Bhāskara, M=Mahāvīra, S=SrīdharaŚrīdhara [sic], C=Chaturveda.