Page:Indian mathematics, Kaye (1915).djvu/79

 60. Multiplier consisting of surds two, three and eight: multiplicand the surd three with the rational number five. Tell quickly the product? Answer—$$\scriptstyle{\sqrt{9}+\sqrt{450}+\sqrt{75}+\sqrt{54}}$$. 61. What is the number which multiplied by five and having the third part of the product subtracted, and the remainder divided by ten; and one-third, one half and a quarter of the original quantity added gives two less than seventy? Answer—48. The solution may be summarised this: $\scriptstyle{f(x)=68}$, $$\scriptstyle{f(3)=17/4}$$ therefore $\scriptstyle{x=\frac{3\times 68}{17/4}=48}$. 62. The eighth part of a troop of monkeys squared was skipping in a grove and delighted with their sport. Twelve remaining were seen on the hill amused with chattering to each other. How many were there in all? Answer—48 or 16. 63. The fifth part of the troop less three, squared, had gone to a cave and one monkey was in sight, having climbed on a branch. Say how many there were? Answer—50 or 5. "But," Bhāskara says, "the second is not to be taken for it is incongruous. People do not approve a negative absolute number." 64. Say quickly what the number is which added to five times itself divided by thirteen becomes thirty? Answer—$$\scriptstyle{\frac{65}{3}}$$. 65. A certain unknown quantity is divided by another. The quotient added to the divisor and the dividend is fifty-three. What is the divisor? Answer—5, 8. L=the Līlāvatī, V=Vīja Gaņita, both by Bhāskara, M=Mahāvīra, S=SrīdharaŚrīdhara [sic], C=Chaturveda.