Question

One-fifth of a hive of bees flew to the ladamba flower,
One-third to the slandbara,
And three times the difference of these two numbers flew to the arbor.
One bee continued to fly about, attracted by the fragrant ketaki and the malati.
What was the number of bees?

Answer 1

Answer:

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Out of a swarm of bees, one fifth settled on a blossom of Kadamba, one third on a flower of Silindhiri, and three times the difference between these two numbers flew to the bloom of Kutaja. Only ten bees were than left the swarm. What was the number of bees in the swarm? (Note, Kadamba, Silindhiri and Kutaja are flowering trees. The problem is from the incident Indian text on algebra.)

Let the number of bees be x.

Bees settled on a blossom of Kadamba =

5

1

x

Bees settled on Silindhiri =

3

1

x

Bees flew to the Kutaja =3(

3

1

−

5

1

)x=(

15

6

)x

The number of bees in the swarm

=x−(

5

1

+

3

1

+

15

6

)x=10

x−

15

14x

=10

15

x

=10

x=150

Hence, this is the answer.