Bhaskaracharya or Bhaskara is one of the most well known mathematicians of ancient India. His masterpiece Siddhanta Siromani, written in 1150 A.D. is divided into four parts -Leelavati (book on arithmetic), Bijaganita (Algebra), Goladhyaya (chapter on sphere i.e. celestial globe), and Grahaganita (mathematics of the planets).

Leelavati is mainly a text book on arithmetic, but it contains some problems on geometry (right angled triangles and mensuration) also. Some authors are of the opinion that Bhaskara named this after his daughter Leelavati (meaning “The Beautiful”). This book contains a number of interesting, poetic problems which give a flavour of ancient Indian school problems.

1. Out of a party of monkeys, the square of one fifth of their number diminished by three went into a cave. The one remaining monkey was climbing up a tree. What is the total number of monkeys?

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We have (\frac{x}{5}-3)^2+1=x, whose two roots are 50 and 5. The answer 5 is inadmissible; so there are 50 monkeys.

2. Out of the swans in a certain lake, ten times the square root of their number went away to Manasa Sarovara when rains started, and one eighth the number went away to the forest Sthala Padmini. Three pairs of swans remained in the tank, engaged in water sports. What is the total number of swans?

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\implies x=144

3. On a pillar 9 cubits high is perched a peacock. From a distance of 27 cubits, a snake is coming to its hole at the bottom of the pillar. Seeing the snake, the peacock pounces upon it. If their speeds are equal, tell me quickly at what distance from the hole is the snake caught?

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\therefore x=12